If a3 + b3 = 20 and a + b = 5, then find the value of a4 + b4.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e 23
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Understanding |
Application |
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Cubing (i) on both sides, (x+y)3= x3+y3+3xy(x+y) Squaring (i) on both sides, (x+y)2= x2+y2+2xy |
a+b= 5 …(i) a3+ b3 + 3ab(a+b) = 125 20+ 3ab×5 = 125 15ab = 125 - 20 15ab = 105 ab = 7 (a+ b)2 = 25 a2+ b2+ 2ab = 25 a2+ b2+ 2×7 = 25 a2+ b2= 25 - 14 a2+ b2 = 11 Again squaring both sides, a4+ b4+ 2a2 b2= 112 a4+ b4+ 2(ab)2= 121 a4+ b4+ 2×(7)2= 121 a4+ b4+ 98 = 121 a4+ b4 = 23 |