Question

If 3a - 4b =10 and ab = -1, find the value of 9a2+16b2 .​

Answer 1

Answer:

The answer of 9a²+16b² is 76.

Step-by-step explanation:

Given: 3a-4b=10 and ab=-1

To find: 9a²+16b²

Solution:

We have two variables a and b and in order to get the values of two unknown variables, we must have two equations as given above.

By applying the property :

(a-b)²=a²+b²-2ab

Here we replace a by 3a and b by 4b

(3a-4b)²=(3a)²+(4b)²-2.3a.4b

3a-4b=10

and ab =-1

so

(10)²=9a²+16b²-24a.b

100=9a²+16b²-24(-1)

100=9a²+16b²+24

So,

9a²+16b²=100-24

9a²+16b²=76

Therefore the answer of 9a²+16b² is 76