Question

12. If 13^3+7^3/13^2+7^2-x= 20, find the value of x.
b) 20
c) 91
d) None of these
a) 6​

Answer 1

Answer:

x = 91

Step-by-step explanation:

Given :

To find the value of x,

When,

$\frac{13^3+7^3}{13^2+7^2-x}=20$

Solution :

We know that,

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

By substituting,

$a =13$ & $b = 7$,

We get,

$13^3+7^3 = (13+7)(13^2 + 7^2 - 13 \times 7) = 20 \times ( 169 + 49 - 91) = 20 \times 127$

By substituting in the given equation,

We get,

$\frac{13^3+7^3}{13^2+7^2-x}=20$

⇒ $\frac{20 \times 127}{169+49-x}=20$

⇒ $\frac{20 \times 127}{218-x}=20$

By cross- multiplication,

We get,

⇒ $20 \times 127 =(218 - x) \times 20$

⇒ $218 - x = 127$

⇒ $x = 218 - 127 = 91$