Question

16. If (3a+ 4b) = 16 and ab = 4; find (9a^2 + 16b^2)

Chapter 3 - Algebra - RS Agarwal - ICSE - Class 9th - Exercise 3 A

Answer 1

Hey there! ☺☻☺

Given,
(3a+4b) = 16
ab = 4

Now,
Squaring both sides,
(3a+4b)² = (16)²
(3a)² + (4b)² + 2 × 3a × 4b = 256
9a² + 16b² + 24 × 4 = 256
9a² + 16b² = 256 - 96
9a² + 16b² = 160   ← (Ans)

Answer 2

Given equation is (3a + 4b) = 16 and ab = 4..

Now,

(3a + 4b) = 16

on squaring both sides, we get

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

9a^2 + 16b^2 + 2 * 3a * 4b = 256

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

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

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

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

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



Hope this helps!