Question

(3х-8)^2 - (4х-6)^2+ (5х-2)(5х+2)>96

Answer 1

${(3x - 8)}^{2} - {(4x - 6)}^{2} + (5x - 2)(5x + 2) > 96 \ (3x - 8 + 4x - 6)(3x - 8 - 4x + 6) + 25 {x}^{2} - 4 > 96 \ (7x - 14)( - x - 2) + 25 {x}^{2} - 4 - 96 > 0 \ - 7(x - 2)(x + 2) + 25 {x}^{2} - 100 > 0 \ - 7( {x}^{2} - 4) + 25( {x}^{2} - 4) > 0 \ 18( {x}^{2} - 4) > 0 \ {x}^{2} - 4 > 0 \ {x}^{2} > 4 \ x > 2 \ x < - 2$
x € (-беск; -2) U (2; + беск)