If $2 a + 3 b = 10$ and $a b = 4$ , then the value of $4 a^{2} + 9 b^{2}$ is equal to

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C 52
Given: $2 a + 3 b = 10$ and $a b = 4$
$∴ 4 a^{2} + 9 b^{2}$
$= (2 a)^{2} + (3 b)^{2}$
$= (2 a + 3 b)^{2} - 2 (2 a) (3 b)$
[ $∵ (a + b)^{2} = a^{2} + b^{2} + 2 a b$ ] $= (2 a + 3 b)^{2} - 12 a b$
$= 10^{2} - 12 \times 4$
$= 100 - 48 = 52$
Hence, the correct answer is option (3).

Suggest Corrections

Similar questions

4 a^{2} - 9 b^{2} - 2 a - 3 b

Factorise:
$4 a^{2} - 9 b^{2} - 2 a - 3 b$

4 a^{2} + 12 a b + 9 b^{2} - 25 c^{2}

2 a + 3 b + 5 c

4 a^{2} + 12 a b + 9 b^{2} - 25 c^{2}

2 a + 3 b + 5 c

3 - 12 (a - b)^{2}

4 a^{2} - 9 b^{2} - 2 a - 3 b

Join BYJU'S Learning Program