Question

Решите неравенство (5х-1)(5х++2)^2< 35

Answer 1

$(5x-1)(5x+1)-(5x+2)^2\ \textless \ 35$

$25x^2-1-(5x+2)^2\ \textless \ 35$

$25x^2-1-(25x^2+4+20x)\ \textless \ 35$

$25x^2-1-25x^2-4-20x\ \textless \ 35$

$-20x-5\ \textless \ 35$

$-20x\ \textless \ 35+5$

$-20x\ \textless \ 40$

$x\ \textgreater \ 40:(-20)$

$x\ \textgreater \ -2$

$x$∈$(-2;+$∞$)$