If a + b = 11 and ab = 35, then what is the value of (a4 + b4)?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 151
Given:
a + b = 11 and ab = 35
Concept used:
1. (a + b)2 = a2 + 2ab + b2
2. a2 + b2 = (a + b)2 - 2ab
Calculation:
a + b = 11
⇒ (a + b)2 = 112 (Taking square on both sides)
⇒ a2 + 2ab + b2 = 121
⇒ (a2 + b2) = 121 - 2 × 35
⇒ (a2 + b2) = 51 ....(1)
Now, (a4 + b4)
⇒ (a2)2 + (b2)2
⇒ (a2 + b2)2 - 2a2b2
⇒ (51)2 - 2 × 352 From (1)
⇒ 151
∴ The required value is 151.