If 2a + 3b = 7 and ab = 2, find 4a2 + 9b2.

If 2a + 3b = 7 and ab = 2, find 4a² + 9b².

Answer :

We know that

(2a + 3b)² = 4a² + 9b² + 12ab

It can be written as

4a² + 9b² = (2a + 3b)² – 12ab

It is given that

2a + 3b = 7

ab = 2

Substituting the values

4a² + 9b² = 7² – 12 × 2

By further calculation

= 49 – 24

= 25

More Solutions:

• If x + y = 6 and x – y = 4, find
• If x – 3 = 1/x, find the value of x2 + 1/x2.
• If x + y = 8 and xy = 3 ¾, find the values of
• Find the value of 2 (x + y)2 + (x – y)2.
• If a – b = 3 and ab = 4, find a3 – b3.
• Find the value of 8a3 – 27b3.
• If x + 1/x = 4, find the values of
• If x – 1/x = 5, find the value of x4 + 1/x4.
• If x – 1/x = √5, find the values of
• If x + 1/x = 6, find