The value of $latex \dfrac {(251)^3 +(249)^3}{25.1 \times 25.1 - 624.99 + 24.9 \times 24.9}$ is $latex 5 \times 10^k$, where the value of k is :

The value of $\dfrac {(251)^3 +(249)^3}{25.1 \times 25.1 - 624.99 + 24.9 \times 24.9}$ is $5 \times 10^k$ , where the value of k is :

Options
a) 4
b) 6
c) 3
d) 5

Solution

As per question
$\dfrac {(251)^3 +(249)^3}{25.1 \times 25.1 - 624.99 + 24.9 \times 24.9} = 5 \times 10^k$

Let value of a = 25.1 and b = 24.9
$\dfrac{(10a)^3 + (10b)^3}{a \times a - ab + b \times b} = \dfrac{10^3(a^3 + b^3)}{a^2 - ab + b^2}= 5 \times 10^k$

Folrmula is: $a^3 + b^3 = (a+b) (a^2 - ab + b^2)$

$\dfrac {10^3 [(a+b) (a^2 - ab + b^2)]}{(a^2 - ab + b^2)}= 5 \times 10^k$
$10^3 (a+b) = 5 \times 10^k$
$10^3 (25.1+24.9) = 5 \times 10^k$
$10^3 (50) = 5 \times 10^k$
$5 \times 10^4 = 5 \times 10^k$
K = 4