Question

: If (a + b) = 9 and ab=14, find the value of a’ -6%.
anmel​

Answer 1

• Appropriate Question

• If (a + b) = 9 and ab=14, find the value of a - b.

• Given

• (a + b) = 9
• ab = 14

• To find

• (a - b)

• Solution

Identity to be used -

$\red{\bigstar}$ $\large {\boxed{\bf {\green{(a + b)^2 = a^2 + b^2 + 2ab}}}}$

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

$\implies\sf{(9)^2 = a^2 + b^2 + 2 \times 14}$

$\implies\sf{81 = a^2 + b^2 + 28}$

$: \implies\sf{81 - 28 = a^2 + b^2}$

$: \implies\sf{53= a^2 + b^2}$

$\red{\bigstar}$ $\large {\boxed{\bf {\green{a^2 + b^2 = 53}}}}$

Identity to be used -

$\green{\bigstar}$ $\large {\boxed{\bf {\blue{(a - b)^2 = a^2 + b^2 - 2ab}}}}$

$: \implies \sf{{(a - b)^2 =53 - 2 \times 14}}$

$: \implies \sf{{(a - b)^2 =53 - 28}}$

$: \implies \sf{{(a - b)^2 =25}}$

$: \implies \sf{{a - b = \sqrt{25} }}$

$: \implies \sf{{a - b = \sqrt{5 \times 5} }}$

$: \implies \sf{{a - b = 5 }}$

$\red{\bigstar}$ $\large {\boxed{\bf {\pink{a - b = 5}}}}$