Question

If 3A + 4 B equal to 16 and AB equal to 4 find the value of 9 a square + 16 b square​

Answer 1

Answer:

160

Step-by-step explanation:

3A+4B = 16

seq. both side

Answer 2

Given,

(3a+4b) = 16

ab = 4

To find,

The value of (9a²+16b²).

Solution,

The value of (9a²+16b²) will be 160.

We can easily solve this problem by following the given steps.

According to the question,

(3a+4b) = 16

Squaring on both sides,

(3a+4b)² = (16)²

Using the identity (a+b)² = a²+b²+2ab to expand the expression,

(Note that in this case a = 3a and b = 4b.)

(3a)²+(4b)²+2(3a)(4b) = 256

9a²+16b²+24ab = 256

We have to find the value of (9a²+16b²). So, moving 24ab from the left-hand side to the right-hand side will result in the change of the sign from plus to minus.

(9a²+16b²) = 256-24ab

Putting the value of ab,

(9a²+16b²) = 256-24(4)

(9a²+16b²) = 256-96

(9a²+16b²) = 160

Hence, the value of (9a²+16b²) is 160.