Question

If a + b = 7 and a2 + b2 = 29, then find the value of ab.

Answer 1

$\bf\large\underline\blue{Question:-}$

• If $a+b=7$ and $a^{2}+b^{2} = 29$, find the value of $ab$

$\bf\large\underline\blue{Solution:-}$

• Before solving, we have to know some identities to solve the problem.

Identity to be used here:-

• ${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$

Now, we will solve the problem.

$a + b = 7$

Squaring both side, we get,

${(a + b)}^{2} = 49$

$\implies {a}^{2} + {b}^{2} + 2ab = 49$

Now, we know that,

${a}^{2} + {b}^{2} = 29$

Putting the value, we get,

$29 + 2ab = 49$

$\implies 2ab = 49 - 29$

$\implies 2ab =20$

$\implies ab = \frac{20}{2}$

$\implies ab =10$

$\bf\large\underline\blue{Answer:-}$

• The value of $ab$ is $10$