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 = 102 ⇒ 4a2 + 9b2 + 2 × 2a × 3b = 100 ⇒ 4a2 + 9b2 + 12ab = 100 ⇒ 4a2 + 9b2 + 12(3) = 100 ⇒ 4a2 + 9b2 + 36 = 100 ⇒ 4a2 + 9b2 = 100 - 36 ⇒ 4a2 + 9b2 = 64 Hence, the correct answer is 64.
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Question : If a3 + b3 = 152 and a + b = 8, then what is the value of ab?
Option 1: 2
Option 2: 11
Option 3: –10
Option 4: 15
Question : If a + b = 8, ab = 10, then the value of a3 + b3 is:
Option 1: 312
Option 2: 215
Option 3: 272
Option 4: 111
Question : If (a – b) = 1, what is the value of (a3 – b3)?
Option 1: a2 + ab + b2
Option 2: (a + b)2 + 3ab
Option 3: a2 – ab + b2
Option 4: a2 + 2ab + b2
Question : If (a – b) = 1 and ab = 6, then what is the value of (a3 – b3)?
Option 1: 21
Option 2: 23
Option 3: 19
Option 4: 25
Question : If 4x2 + y2 = 40 and xy = 6, then find the value of 2x + y.
Option 1: 6
Option 2: 8
Option 3: 5
Option 4: 4
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