Question

Find the value of
(.555 *.555 - .555 *.020 +
020 ~ .020)/
(.555.555 ~ .555) + (.020
.020 .020)
(A) 1.55
(B) 1.74
(C) 2.36
(D)5.02​

Answer 1

$\textbf{Given:}$

$\mathrm{\dfrac{0.555{\times}0.555-0.555{\times}0.020+0.020{\times}0.020}{0.555{\times}0.555{\times}0.555+0.020{\times}0.020{\times}0.020}}$

$\textbf{To find:}$

$\text{The value of}$

$\mathrm{\dfrac{0.555{\times}0.555-0.555{\times}0.020+0.020{\times}0.020}{0.555{\times}0.555{\times}0.555+0.020{\times}0.020{\times}0.020}}$

$\textbf{Solution:}$

$\text{Consider,}$

$\mathrm{\dfrac{0.555{\times}0.555-0.555{\times}0.020+0.020{\times}0.020}{0.555{\times}0.555{\times}0.555+0.020{\times}0.020{\times}0.020}}$

$\mathrm{=\dfrac{(0.555)^2-0.555{\times}0.020+(0.020)^2}{(0.555)^3+(0.020)^3}}$

$\text{Using the identity}$

$\boxed{\mathrm{\bf\,a^3+b^3=(a+b)(a^2-ab+b^2)}}$

$\mathrm{=\dfrac{(0.555)^2-0.555{\times}0.020+(0.020)^2}{(0.555+0.020)((0.555)^2-0.555{\times}0.020+(0.020)^2)}}$

$\mathrm{=\dfrac{1}{0.555+0.020}}$

$\mathrm{=\dfrac{1}{0.575}}$

$\mathrm{=\dfrac{1000}{575}}$

$\mathrm{=1.74}$

$\implies\mathrm{\dfrac{0.555{\times}0.555-0.555{\times}0.020+0.020{\times}0.020}{0.555{\times}0.555{\times}0.555+0.020{\times}0.020{\times}0.020}=1.74}$

$\textbf{Answer:}$

$\textbf{Option (B) is correct}$

Find more:

P+p²+p³+p⁴+p⁵+p⁶+p⁷)/(p⁻³+p⁻⁴+p⁻⁵+p⁻⁶+p⁻⁷+p⁻⁸+p⁻⁹)

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