Đáp án:
Bài `1.`
`a, x= 3/4`
`b,x=7/2` hoặc `x=5/2`
`c, x=(-3)/2`
Bai `2.`
`A = 2^{18}`
`B=256`
Bài `3.`
`2^2 + 4^2 + 6^2 + ... + 20^2 = 1540` khi `1^2 + 2^2 + ... + 10^2=385`
Giải thích các bước giải:
Bài `1.`
`a,`
`(x-3/4)^2=0`
`⇔ x - 3/4=0`
`⇔x=0+3/4`
`⇔x=3/4`
Vậy `x=3/4`
`b,`
`(x-3)^2=1/4`
`⇔` \(\left[ \begin{array}{l}(x-3)^2=(\dfrac{1}{2})^2\\(x-3)^2=(\dfrac{-1}{2})^2\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x-3=\dfrac{1}{2}\\x-3=\dfrac{-1}{2}\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=\dfrac{1}{2}+3\\x=\dfrac{-1}{2}+3\end{array} \right.\)
`⇔` \(\left[ \begin{array}{l}x=\dfrac{7}{2}\\x=\dfrac{5}{2}\end{array} \right.\)
Vậy `x=7/2` hoặc `x=5/2`
`c,`
`(2x+1)^3=-8`
`⇔ (2x+1)^3=(-2)^3`
`⇔2x+1=-2`
`⇔2x=-2-1`
`⇔2x=-3`
`⇔x=-3÷2`
`⇔ x= (-3)/2`
Vậy `x=(-3)/2`
Bài `2.`
`A = 8^{14}/4^{12}`
`⇔ A = (2^3)^{14}/(2^2)^{12}`
`⇔ A = 2^{42}/2^{24}`
`⇔ A = 2^{18}`
Vậy `A=2^{18}`
`B = (8^{10} + 4^{10})/(8^4 + 4^{11})`
`⇔ B = ( (2^3)^{10} + (2^2)^{10})/( (2^3)^4 + (2^2)^{11})`
`⇔ B = (2^{30} + 2^{20})/(2^{12} + 2^{22})`
`⇔ B = (2^{20} (2^{10} + 1) )/(2^{12} (2^{20} + 1) )`
`⇔B = 2^{20}/2^{12}`
`⇔B=2^8`
`⇔B=256`
Vậy `B=256`
Bài `3.`
`2^2 + 4^2 + 6^2 + ... + 20^2`
`= (1×2)^2 + (2×2)^2 + (2×3)^2 + ... + (2×10)^2`
`= 1^2 × 2^2 + 2^2 × 2^2 + 2^2 × 3^2 + ... + 2^2 × 10^2`
`= 2^2 × (1^2 + 2^2 + 3^2 + ... + 10^2)`
mà `1^2 + 2^2 + 3^2 + ... + 10^2 = 385`
`= 2^2 × 385`
`= 4 × 385`
`= 1540`
Vậy `2^2 + 4^2 + 6^2 + ... + 20^2 = 1540` khi `1^2 + 2^2 + ... + 10^2=385`
