√27 * 3^(-6x^2) ≥ 9^4x степенное неравенство,! - вопрос №27362945326438 от ArthurMyChemov 07.11.2020 21:27

Question

Математика: √27 * 3^(-6x^2) ≥ 9^4x степенное неравенство,!

ArthurMyChemov · Answer

√ 27 * 3 ^ ( - 6X^2 ) ≥ 9 ^ 4X
( 3 ^ 3 ) ^ 1/2 * 3 ^ ( - 6X^2 ) ≥ ( 3 ^ 2 ) ^ 4X
3 ^ 3/2 * 3 ^ ( - 6X^2 ) ≥ 3 ^ 8x
3 ^ ( 3/2 - 6X^2 ) ≥ 3 ^ 8X
3/2 - 6X^2 ≥ 8X
3 - 12X^2 ≥ 16X
- 12X^2 - 16X + 3 ≥ 0
D = 256 + 144 = 400 ; √ D = 20
X1 = ( 16 + 20 ) : ( - 24 ) = - 1,5
X2 = ( 16 - 20 ) : ( - 24 ) = + 4/24 = 1/6
( X + 1,5 )*( X - ( 1/6 ) ) ≥ 0