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If (a2 + 1)(b2 + 1) + 36 = 12(a + b), find a4 + b
1. 1158
2. 1028
3. 1064
4. 1154

1 Answer

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Best answer
Correct Answer - Option 4 : 1154

Given:

(a2 + 1)(b2 + 1) + 36 = 12(a + b)

Formula used:

(a + b)2 = a2 + b2 + 2ab

(a – b)2 = a2 + b2 – 2ab

Calculation:

According to the question,

⇒ (a2 + 1)(b2 + 1) + 36 = 12(a + b)

⇒ a2b2 + a2 + b2 + 1 + 36 – 12(a + b) = 0

Subtracting 2ab from both the sides,

⇒ a2b2 + a2 + b2 + 1 + 36 – 12(a + b) – 2ab = – 2ab

⇒ a2b2 + 1 – 2ab + a2 + b2 + 2ab + 36 – 12(a + b) = 0

⇒ (ab – 1)2 + (a + b)2 + 36 – 12(a + b) = 0

⇒ (ab – 1)2 + (a + b - 6)2 = 0

As square cannot be negative,

⇒ ab – 1 = 0

⇒ ab = 1

Also,

⇒ a + b – 6 = 0

⇒ a + b = 6

Squaring both sides,

⇒ (a + b)2 = 62

⇒ a2 + b2 + 2ab = 36

⇒ a2 + b2 + 2(1) = 36

⇒ a2 + b2 = 36 – 2

⇒ a2 + b2 = 34

Again, Squaring

⇒ (a2 + b2)2= (34)2

⇒ a4 + b4 + 2a2b2 = 1156

⇒ a4 + b4 + 2(1)2 = 1156

⇒ a4 + b4 = 1156 – 2

⇒ a4 + b4 = 1154

The value of a4 + b4 is 1154 

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