Bài 6:
`(x+ 5)^3 = - 64`
`⇔(x+5)^3=(-4)^3`
`⇔x+5=-4`
`⇔x=-4-5`
`⇔x=-9.`
Vậy `x=-9.`
`b)(2x- 3)^2 = 9`
`⇔(2x-3)^2=3^2=(-3)^2`
`⇒` \(\left[ \begin{array}{l}2x-3=3\\2x-3=-3\end{array} \right.\)
`⇒` \(\left[ \begin{array}{l}2x=6\\2x=0\end{array} \right.\)
`⇒` \(\left[ \begin{array}{l}x=3\\x=0\end{array} \right.\)
Vậy `x∈{3;0}.`
Bài 7:
`frac{8^{10}+4^{10}}{8^{4}+4^{11}}`
`=frac{(2^3)^{10}+(2^2)^{10}}{(2^3)^{4}+(2^2)^{11}}`
`=frac{2^{30}+2^{20}}{2^{12}+2^{22}}`
`=frac{2^{20}.(2^{10}+1)}{2^{12}.(1+2^{10})}`
`=frac{2^{20}}{2^{12}}`
`=2^8=256.`
Bài 8:
`12.20 =15.16`
`⇒ 12/15 = 16/20 `
`⇔ 20/15 = 16/12`
`⇔ 15/20=12/16`
`⇔ 15/12=20/16...`
Bài 10:
Theo bài ra ta có: `x/y=2/5⇔x/2=y/5` `,x+y=70.`
Áp dụng tính chất của dãy tỉ số bằng nhau ta có:
`x/2=y/5=\frac{x+y}{2+5}=70/7=10.`
`⇒ x/2 = 10 ⇒ x=10.2=20`
`⇒ y/5 =10 ⇒ y= 5.10 =50`
Vậy `x=20, y=50.`
