Question

if a+b=8 and ab=7. Evaluate a4+a2b2+b4

Answer 1

∧a + b = 8
squaring both sides
a²+b²+2ab =8²
a²+b² +2×7 = 64
a²+b² = 64-14
a²+b² = 50
squaring both sides
a^4 + b^4 +2a²b² = 50²
a^4 +b^4 +2×49 =2500
a^4+b^4 = 2500-98
a^4 + b^4 = 2402
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