Question

If (a+b) =12 and ab=14,then (a^2+b^2)=?

Answer 1

${a}^{2} + {b}^{2} \\ = {(a + b)}^{2} - 2ab \\ = {12 }^{2} - 2 \times 14 \\ = 144 - 28 \\ = 116$
so, a^2+b^2 = 116

Answer 2

The value of $(a^2+b^2)=116$

Step-by-step explanation:

Given,

a + b = 12 and ab = 14

To find, the value of $(a^2+b^2)=?$

We know that,

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

⇒ $a^{2}+b^{2}=(a+b)^{2}-2ab$

Put a + b = 12 and ab = 14, we get

$a^{2}+b^{2}=12^{2}-2(14)$

⇒ $a^{2}+b^{2}=144-28$

⇒ $a^{2}+b^{2}=116$

The value of $(a^2+b^2)=116$

Hence, the value of $(a^2+b^2)=116$