`a)`
`16x^2 - (4x-5)^2 = 15`
`=> 16x^2 - [ (4x)^2 - 2 . 4x . 5 + 5^2] = 15`
`=> 16x^2 - (16x^2 - 40x + 25) = 15`
`=> 16x^2 - 16x^2 + 40x - 25 = 15`
`=> 40x - 25 = 15`
`=> 40x = 40`
`=> x=1`
Vậy `x=1`
`b)`
`(2x+3)^2- 4(x-1)(x+1) = 49`
`=> [ (2x)^2 + 2 . 2x . 3 + 3^2] - 4 (x^2 - 1) = 49`
`=> (4x^2 + 12x + 9) - 4x^2 + 4 = 49`
`=> 4x^2 + 12x + 9 -4x^2 + 4 = 49`
`=> 12x + 13 = 49`
`=> 12x = 36
`=> x = 3`
Vậy `x=3`
`c)`
`(2x+1)(1-2x) + (1-2x)^2 = 18`
`=> [ 1^2 - (2x)^2 ] + [ 1^2 - 2 . 1 . 2x + (2x)^2] = 18`
`=> (1 - 4x^2) + (1 - 4x + 4x^2) = 18`
`=> 1 - 4x^2 + 1 - 4x + 4x^2 = 18`
`=> 2-4x =18`
`=> 4x = -16`
`=> x = -4`
Vậy `x=-4`
`d)`
`2 (x+1)^2 - (x-3)(x+3) - (x-4)^2 = 0`
`=> 2 (x^2 + 2x + 1) -(x^2 - 3^2) - (x^2 - 2 . x . 4 + 4^2) = 0`
`=> 2x^2 + 4x + 2 - (x^2 - 9) - (x^2 - 8x + 16) = 0`
`=> 2x^2 + 4x + 2 - x^2 + 9 - x^2 + 8x - 16 = 0`
`=> (2x^2 - x^2 - x^2) + (4x + 8x) + (2+9-16)=0`
`=> 12x -5=0`
`=> 12x=5`
`=>x=5/12`
Vậy `x=5/12`
`e)`
`(x-5)^2 - x(x-4) = 9`
`=> (x^2 - 2 . x . 5 + 5^2) - (x^2 - 4x ) = 9`
`=> x^2 - 10x + 25 - x^2 + 4x = 9`
`=> -6x + 25 = 9`
`=> -6x = -16`
`=> x = 8/3`
Vậy `x=8/3`
`f)`
`(x-5)^2 - (x-4)(1-x) = 0`
`=> (x^2 - 2 . x . 5 + 5^2) - (x - x^2 - 4 + 4x) = 0`
`=> x^2 - 10x + 25 - x + x^2 + 4 - 4x= 0 `
`=> 2x^2 -15x + 29 = 0`
`=> 2 (x^2 - 15/2x + 225/16) + 7/ 8 =0`
`=> 2 [ x^2 - 2 . x . 15/4 + (15/4)^2] + 7/ 8=0`
`=> 2 (x - 15/4)^2 + 7/8=0`
`\forall x` ta có :
`(x-15/4)^2 \ge 0`
`=> 2(x-15/4)^2 \ge 0`
`=> 2(x-15/4)^2 + 7/8 \ge 7/8 > 0`
`=> 2x^2 - 15x + 29 \ne 0`
Vậy không tìm được `x` thỏa mãn yêu cầu đề bài.