Question

Value of the expression $\frac{8.73\times 8.73\times 8.73+4.27\times 4.27\times 4.27}{8.73\times 8.73-8.73\times 4.27+4.27\times 4.27}$ is

• A. $8.73$
• B. $4.27$
• C. $4.46$
• D. $13$

Answer 1

The correct option is D $13$

Let us assume that $a=8.73$ and $b=4.27$ and substitute the values in the expression $\frac{8.73\times 8.73\times 8.73+4.27\times 4.27\times 4.27}{8.73\times 8.73-8.73+4.27+4.27\times 4.27}$ as follows:

$\frac{8.73\times 8.73\times 8.73+4.27\times 4.27\times 4.27}{8.73\times 8.73-8.73\times 4.27+4.27\times 4.27}=\frac{a\times a\times a+b\times b\times b}{a\times a-a\times b+b\times b}=\frac{a^3+b^3}{a^2-ab+b^2}=\frac{{(a+b)(a}^2+b^2-ab)}{a^2-ab+b^2}=a+b$

Now substituting $a=8.73$ and $b=4.27$ in $a+b$ we get,

$a+b=8.73+4.27=13$.

Hence, the expression $\frac{8.73\times 8.73\times 8.73+4.27\times 4.27\times 4.27}{8.73\times 8.73-8.73+4.27+4.27\times 4.27}=13$