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- (a^2 + b^2)(a^3 + b^3) = a^5 + a^3b^2 + a^2b^3 + b^5
- = a^5 + b^5 + a^2b^2(a + b)
- 3x1^2x2 +3x1x2^2 = 3(x1^2x2 + x1x2^2) = 3(x1x2(x1+x2))
- -----------------------------------------------------------
- x^2-x-3=0
- x1 + x2 =1
- x1 * x2 = -3
- (x1 +x2) ^ 2 = x1^2 + x2^2 + 2(x1x2)
- 1 = x1^2 + x2^2 + (-6)
- 7 = x1^2 + x2^2
- (x1 +x2) ^ 3 = x1^3 + x2^3 + 3x1^2x2 +3x1x2^2
- 1 = x1^3 + x2^3 + 3(x1^2x2 + x1x2^2)
- 1 = x1^3 + x2^3 + 3(x1x2(x1+x2))
- 1 = x1^3 + x2^3 + 3((-3)(1)
- 1 = x1^3 + x2^3 + 3((-3)(1)
- 1 = x1^3 + x2^3 + (-9)
- 10 = x1^3 + x2^3
- (a^2 + b^2)(a^3 + b^3) = a^5 + a^3b^2 + a^2b^3 + b^5
- = a^5 + b^5 + a^2b^2(a + b)
- (7) (10) = a^5 + b^5 + (ab)^2(a+b)
- 70 = a^5 + b^5 + (-3)^2(1)
- 70 = a^5 + b^5 + 9
- 61 = a^5 + b^5
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