Đáp án+Giải thích các bước giải:
`39.`
`a)36-12x+x^2`
`=6^2-2.6.x+x^2`
`=(6-x)^2`
`b)4x^2+12x+9`
`=(2x)^2+2.2x.3+3^2`
`=(2x+3)^2`
`c)-25x^6-y^8+10x^3 y^4`
`=-(25x^6-10x^3 y^4+y^8)`
`=-[(5x^3)^2-2.5x^3 .y^4+(y^4)^2]`
`=-(5x^3-y^4)`
`d)1/4 x^2-5xy+25y^2`
`=(1/2x)^2+2.1/2x .5y+(5y)^2`
`=(1/x+5y)^2`
`40.`
`a)(x-5)^2-16`
`=(x-5)^2-4^2`
`=(x-5-4)(x-5+4)`
`=(x-9)(x-1)`
`b)25-(3-x)^2`
`=5^2-(3-x)^2`
`=(5-3+x)(5+3-x)`
`=(2+x)(8-x)`
`c)(7x-4)^2-(2x+1)^2`
`=(7x-4-2x-1)(7x-4+2x+1)`
`=(5x-5)(9x-3)`
`=15(x-1)(3x-1)`
`d)49(y-4)^2-9(y+2)^2`
`=[7(y-4)-3(y+2)][7(y-4)+3(y+2)]`
`=(7y-28-3y-6)(7y-28+3y+6)`
`=(4y-34)(10y-22)`
`=4(2y-17)(5y-11)`
`e)8x^3+1/27`
`=(2x+1/3)(4x^2-2/3x+1/9)`
`f)125-x^6`
`=5^3-(x^2)^2`
`=(5-x^2)(5+x^2)`
`41`
`a)(x-4)^2-36=0`
`<=>(x-4)^2-6^2=0`
`<=> (x-4-6)(x-4+6)=0`
`<=> (x-10)(x+2)=0`
`<=>`\(\left[ \begin{array}{l}x-10=0\\x+2=0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=10\\x=-2\end{array} \right.\)
Vậy `x ∈{10;-2}`
`b)(x+8)^2=121`
`<=> x+8=±11`
`<=>`\(\left[ \begin{array}{l}x+8=11\\x+8=-11\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=3\\x=-19\end{array} \right.\)
Vậy `x ∈ {3;-19}`
`c)x^2+8x+16=0`
`<=> (x+4)^2=0`
`<=> x+4=0`
`<=> x=-4`
Vậy `x=-4`
`d)4x^2-12x=-9`
`<=> 4x^2-12+9=0`
`<=> (2x+3)^2=0`
`<=> 2x+3=0`
`<=> 2x=-3`
`<=> x=-3/2`
Vậy `x=-3/2`
