Question

3a+4b = 16 & ab=4,find the value of 9a^2 +16b^2

Answer 1

9a^2+16b^2
= (3a)^2+(4b)^2
= (3a+4b)^2 - 2×3a×4b
= (3a+4b)^2 - 24ab
= (16)^2 - 24×4
= 256 - 96
= 160 ans......
I hope you will understand ..

Answer 2

Answer:

$\text{The value of }9a^2+16b^2\text{ is }160$

Step-by-step explanation:

Given that 3a+4b = 16 & ab=4,

$\text{we have to find the value of } 9a^2 +16b^2$

$3a+4b = 16$

Squaring on both sides, we get

$(3a+4b)^2=16^2$

$\text{As }(a+b)^2=a^2+b^2+2ab$

$9a^2+16b^2+2(3a)(4b)=256$

$9a^2+16b^2+24ab=256$

$9a^2+16b^2+24(4)=256$

$9a^2+16b^2=256-96$

$9a^2+16b^2=160$

$\text{Hence, the value of }9a^2+16b^2\text{ is }160$