Đáp án:
`↓↓`
Giải thích các bước giải:
`1.`
`a, M = t(10 - 4t) - t^2(2t - 5) - 2t + 5`
`= 2t(2t - 5) - t^2(2t - 5) - (2t - 5)`
`=(2t - t^2 - 1)(2t - 5)`
`\text{Tại t}` `= 5/2` `\text{Ta có :}`
`[2.5/2 - (5/2)^2 - 1](2.5/2 - 5) = [2.5/2 - (5/2)^2 - 1](5 - 5) = [2.5/2 - (5/2)^2 - 1].0 = 0`
`b, x^2(y - 1) - 5x(1 - y)` `= x^2(y - 1) - [-5x(y - 1)]`
`= x^2(y - 1) + 5x(y - 1)`
`= (y - 1)(x^2 + 5x)`
`= (y - 1)x(x + 5)`
`\text{Thay}` `x = -20` `\text{và}` `y = 1001` `\text{ta có :}`
`= (1001 - 1).(-20).(-20 + 5) = 1000.(-20).(-15) = 1000.300 = 300000`
`c, P = y^2(x^2 + y - 1) - mx^2 - my + m`
`= y^2(x^2 + y - 1) - (mx^2 + my - m)`
`= y^2(x^2 + y - 1) - m(x^2 + y - 1)`
Không có kết quả câu b.
`2.`
`a, 8x(x - 2017) - 2x + 4034 = 0`
`=> 8x(x - 2017) - (2x - 4034) = 0`
`=> 8x(x - 2017) - 2(x - 2017) = 0`
`=> (8x - 2)(x - 2017) = 0`
`=> 8x - 2 = 0 hoặc x - 2017 = 0`
`=> x = 1/4 hoặc x = 2017`
`b, x/2 + x^2/8 = 0`
`=> 4x/8 + x^2/8 = 0`
`=> (4x + x^2)/8 = 0`
`=> 4x+ x^2 = 0`
`=> x^2 + 4x = 0`
`=> x(x + 4) = 0`
`=> x = 0` `\text{hoặc}` `x + 4 = 0`
`=> x = 0` `\text{hoặc}` `x = -4
`c, 4 - x = 2(x - 4)^2`
`=> 4 - x = 2(x^2 - 8x + 16)`
`=> 4 - x = 2x^2 - 16x + 32`
`=> 4 - x - 2x^2 + 16x - 32 = 0`
`=> (4 - 32)+(-x + 16x) - 2x^2 = 0`
`=> -28 + 15x - 2x^2 = 0`
`=> -2x^2 + 15x - 28 = 0`
`=> -2(x^2 - 15/2x + 14) = 0`
`=> -2[x^2 - 2.x.15/4 + (15/4)^2] + 1/8 = 0`
`=> -2(x - 15/4)^2 + 1/8 = 0`
`=> -2(x - 15/4)^2 = -1/8`
`=> (x - 15/4)^2 = 1/16`
`=> (x - 15/4)^2 - 1/16 = 0`
`=> (x - 15/4)^2 - (1/4)^2 = 0`
`=> (x - 15/4 - 1/4)(x - 15/4 + 1/4) = 0`
`=> (x - 4)(x - 7/2) = 0`
`=> x = 4` `\text{hoặc}` `x = 7/2`
`3.`
`a, x^4 - 16x^2 = 0`
`=> x^2(x^2 - 16) = 0`
`=> x^2(x - 4)(x + 4) = 0`
`=> x^2 = 0 , x - 4 = 0 , x + 4 = 0`
`=> x = 0 , x = 4 , x = -4`
`b, x^8 + 36x^4 = 0`
`=> x^4(x^4 + 36) = 0`
`=> x^4 = 0`
`=> x = 0`
`c, (x - 5)^3 - x + 5 = 0`
`=> (x - 5)(x - 5)^2 - (x - 5) = 0`
`=> (x - 5)(x - 5)^2 - 1(x - 5) = 0`
`=> (x - 5)[(x - 5)^2 - 1] = 0`
`=> (x - 5)[(x - 5)^2 - 1^2] = 0`
`=> (x - 5)(x - 5 - 1)(x - 5 +1) = 0`
`=> (x - 5)(x - 6)(x - 4) = 0`
`=> x = 5 , x = 6 , x = 4`
`d, 5(x - 2) - x^2 + 4 = 0`
`=> 5(x - 2) - (x^2 - 4) = 0`
`=> 5(x - 2) - (x + 2)(x - 2) = 0`
`=> (x - 2)[5 - (x + 2)] = 0`
`=> x = 2` `\text{hoặc}` `5 - (x + 2) = 0`
`=> x = 2` `\text{hoặc}` `x + 2 = 5`
`=> x = 2` `\text{hoặc}` `x = 3`
Học tốt!!!
