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Ответ:

udalda520udalda

29.12.2022

1) (a + x)² = a² + 2ax + x²;
2) (x + 2)² = x² + 4x + 4;
3) (y - 1)² = y² - 2y + 1;
4) (5 - p)² = 25 - 10p + p²;
5) (4 + k)² = 16 + 8k + k²;
6) (3a - 2)² = 9a² - 12a + 4;
7) (7b + 6)² = 49b² + 84b + 36;

4,5(31 оценок)

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Ответ:

WaysWhite

29.12.2022

(x^2 + x + 4)^2 + 8x(x^2 + x + 4) = - 15x^2
(x^2 + x + 4)(x^2 + x + 4 + 8x) = - 15x^2
(x^2 + x +4)(x^2 +9x + 4) = - 15x^2
x^4 + 9x^3 + 4x^2 + x^3 + 9x^2 + 4x + 4x^2 + 36x + 16 + 15x^2 = 0
x^4 + 10x^3 + 32x^2 + 40x + 16 =0
( x+ 2)^2(x^2 + 6x + 4) = 0
(x + 2)(x + 2)(x^2 + 6x + 4) = 0
x + 2 = 0
x = - 2
x + 2 = 0
x = - 2
x^2 + 6x + 4 = 0
D = b^2 - 4ac =36 - 16 = 20
x1 = ( - 6 + 2√5) / 2 = - 2(3 - √5) / 2 = - (3 - √5) = √5 - 3
x2 = ( - 6 - 2√5) / = - 2(3 + √5)/ 2 = - (3 + √5) = - 3 - √5
ответ: x1 = √5 - 3,x2 = -√5 - 3, x3 = - 2,x4 = - 2

4,4(9 оценок)

Ответ:

Dima25688

29.12.2022

-a4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4 ————————————————————————————————————————————————————————————————————————————————————————————— (a-b)•(b-c)•(c-a) Reformatting the input :

Changes made to your input should not affect the solution:

(1): "c2" was replaced by "c^2". 2 more similar replacement(s).

Step by step solution :Skip Ad
Step 1 : c2 Simplify ————— c - a Equation at the end of step 1 : (a2) (b2) c2 ((—————•(a-c))+(—————•(b-a)))+(———•(c-b)) (a-b) (b-c) c-a Step 2 :Equation at the end of step 2 : (a2) (b2) c2•(c-b) ((—————•(a-c))+(—————•(b-a)))+———————— (a-b) (b-c) c-a Step 3 : b2 Simplify ————— b - c Equation at the end of step 3 : (a2) b2 c2•(c-b) ((—————•(a-c))+(———•(b-a)))+———————— (a-b) b-c c-a Step 4 :Equation at the end of step 4 : (a2) b2•(b-a) c2•(c-b) ((—————•(a-c))+————————)+———————— (a-b) b-c c-a Step 5 : a2 Simplify ————— a - b Equation at the end of step 5 : a2 b2•(b-a) c2•(c-b) ((———•(a-c))+————————)+———————— a-b b-c c-a Step 6 :Equation at the end of step 6 : a2•(a-c) b2•(b-a) c2•(c-b) (————————+————————)+———————— a-b b-c c-a Step 7 :Calculating the Least Common Multiple :

7.1    Find the Least Common Multiple

      The left denominator is :       a-b

      The right denominator is :       b-c

                  Number of times each Algebraic Factor
            appears in the factorization of:    Algebraic
    Factor     Left
Denominator  Right
Denominator  L.C.M = Max
{Left,Right}  a-b 101 b-c 011

Least Common Multiple:
(a-b) • (b-c)

Calculating Multipliers :

7.2    Calculate multipliers for the two fractions

    Denote the Least Common Multiple by  L.C.M
    Denote the Left Multiplier by  Left_M
    Denote the Right Multiplier by  Right_M
    Denote the Left Deniminator by  L_Deno
    Denote the Right Multiplier by  R_Deno

   Left_M = L.C.M / L_Deno = b-c

   Right_M = L.C.M / R_Deno = a-b

Making Equivalent Fractions :

7.3 Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. a2 • (a-c) • (b-c) —————————————————— = —————————————————— L.C.M (a-b) • (b-c) R. Mult. • R. Num. b2 • (b-a) • (a-b) —————————————————— = —————————————————— L.C.M (a-b) • (b-c) Adding fractions that have a common denominator :

7.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

a2 • (a-c) • (b-c) + b2 • (b-a) • (a-b) a3b - a3c - a2b2 - a2bc + a2c2 + 2ab3 - b4 ——————————————————————————————————————— = —————————————————————————————————————————— (a-b) • (b-c) (a - b) • (b - c) Equation at the end of step 7 : (a3b - a3c - a2b2 - a2bc + a2c2 + 2ab3 - b4) c2 • (c - b) ———————————————————————————————————————————— + ———————————— (a - b) • (b - c) c - a Step 8 :Calculating the Least Common Multiple :

8.1    Find the Least Common Multiple

      The left denominator is :       (a-b) • (b-c)

      The right denominator is :       c-a

                  Number of times each Algebraic Factor
            appears in the factorization of:    Algebraic
    Factor     Left
Denominator  Right
Denominator  L.C.M = Max
{Left,Right}  a-b 101 b-c 101 c-a 011

Least Common Multiple:
(a-b) • (b-c) • (c-a)

Calculating Multipliers :

8.2    Calculate multipliers for the two fractions

    Denote the Least Common Multiple by  L.C.M
    Denote the Left Multiplier by  Left_M
    Denote the Right Multiplier by  Right_M
    Denote the Left Deniminator by  L_Deno
    Denote the Right Multiplier by  R_Deno

   Left_M = L.C.M / L_Deno = c-a

   Right_M = L.C.M / R_Deno = (a-b)•(b-c)

Making Equivalent Fractions :

8.3 Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. (a3b-a3c-a2b2-a2bc+a2c2+2ab3-b4) • (c-a) —————————————————— = ———————————————————————————————————————— L.C.M (a-b) • (b-c) • (c-a) R. Mult. • R. Num. c2 • (c-b) • (a-b) • (b-c) —————————————————— = —————————————————————————— L.C.M (a-b) • (b-c) • (c-a) Adding fractions that have a common denominator :

8.4 Adding up the two equivalent fractions

(a3b-a3c-a2b2-a2bc+a2c2+2ab3-b4) • (c-a) + c2 • (c-b) • (a-b) • (b-c) -a4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4 ————————————————————————————————————————————————————————————————————— = ————————————————————————————————————————————————————————————————————————————————————————————— (a-b) • (b-c) • (c-a) (a-b) • (b-c) • (c-a) Final result : -a4b+a4c+a3b2+2a3bc-2a3c2-2a2b3-a2b2c-a2bc2+a2c3+ab4+2ab3c-ab2c2+2abc3-ac4-b4c+b3c2-2b2c3+bc4 ————————————————————————————————————————————————————————————————————————————————————————————— (a-b)•(b-c)•(c-a)

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Latest drills solved(-4,7)to(94,-55)(5)/(7)+(4)/(y)=38(x+8/9)-9a2/(a-b)(a-c)+b2/(b-c)(b-a)+c2/(c-a)(c-b)

4,7(75 оценок)

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