Question

The value of $\frac{5.35\times{5.35}\times{5.35}+3.65\times{3.65}\times{3.65}}{53.5\times{53.5}+36.5\times{36.5}-53.5\times{36.5}}$ is:

• A. 9
• B. 0.9
• C. 90
• D. 0.09

Answer 1

Answer:

D. 0.09

Solution:

Identity used:

(a³ + b³) = (a + b) × (a² + b² – ab)

Calculation:

$\frac{5.35\times{5.35}\times{5.35}+3.65\times{3.65}\times{3.65}}{53.5\times{53.5}+36.5\times{36.5}-53.5\times{36.5}}$

$⇒\frac{(5.35)^3+(3.65)^3}{(53.5)^2+(36.5)^2-53.5\times{36.5}}$

$⇒\frac{(5.35)^3+(3.65)^3}{100\times[{(5.35)^2+(3.65)^2-5.35\times{3.65}}]}$

ie., $\frac{a^3+b^3}{a^2+b^2-ab}=a+b$

Here $a=5.35 ,b= 3.65$

$⇒\frac{5.35+3.65}{100}$

$⇒ \frac{9}{100}$

∴ 0.09