Question

if (3a+4b)=16 and ab =4 find (9a²+16b²) Pls explain well​

Answer 1

Answer: 160

Step-by-step explanation:

(3a+4b)²=(3a)²+(4b)²+2(3a)(4b)

{x+y}²=x²+y²+2xy

(3a+4b)²=9a²+16b²+24ab

(16)²=9a²+16b²+24(4)

256=9a²+16b²+96

9a²+16b²=256-96

9a²+16b²=160

Answer 2

We will use an identity to solve this question.

( x + y )² = x² + y² + 2xy

Here, x = 3a, y = 4b and xy = ab = 4
Most importantly ( 3a + 4b ) = 16

Now,
Substituting the values in the given equation,
( 3a + 4b )² = (3a)² + (4b)² + 2 * ( 3a ) * ( 4b )

Performing simple multiplication,

=> 16² = 9a² + 16b² + 24ab

Substituting values,

=> 256 = 9a² + 16b² + 24 * ( 4 )

Performing multiplication in RHS and shifting the same to LHS,

=> 9a² + 16b² = 256 - 96

Performing simple subtraction,

=> 9a²+ 16b² = 160