Question

a2-b2=10 , ab=4 then a4+b4=?

Answer 1

Answer:

Value of $a^4+b^4=132$

Step-by-step explanation:

Given: $a^2-b^2=10, ab=4$

W have to find the value of $a^4+b^4$

Consider,

$a^2-b^2=10$

Squaring both sides, we get,

$(a^2-b^2)^2=(10)^2$

Applying identity $(a-b)^2=a^2+b^2-2ab$ , we get,

$a^4+b^4-2a^2b^2=100$

Using $a^2b^2=(ab)^2$

$a^4+b^4-2(ab)^2=100$

We know, value of ab = 4

$\Rightarrow a^4+b^4-2(4)^2=100$

$\Rightarrow a^4+b^4-32=100$

$\Rightarrow a^4+b^4=100+32$

$\Rightarrow a^4+b^4=132$

Hence, value of $a^4+b^4=132$