Question : If 2a + 3b = 10 and ab = 3, then find the value of 4a2 + 9b2.
Option 1: 60
Option 2: 62
Option 3: 64
Option 4: 68
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Correct Answer: 64
Solution :
Given, 2a + 3b = 10
Squaring both sides,
(2a + 3b)
2
= 10
2
⇒ 4a
2
+ 9b
2
+ 2 × 2a × 3b = 100
⇒ 4a
2
+ 9b
2
+ 12ab = 100
⇒ 4a
2
+ 9b
2
+ 12(3) = 100
⇒ 4a
2
+ 9b
2
+ 36 = 100
⇒ 4a
2
+ 9b
2
= 100 - 36
⇒ 4a
2
+ 9b
2
= 64
Hence, the correct answer is 64.
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