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(x ^ 2 - y ^ 2)/(xy) = (x + y)/11 = (x - y)/5 |
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Answer» Answer: Step-by-step explanation: x²+y=7 x+y²=11 y²=11-x (x²+y)²=7² x⁴+2x²y+y²=49 [INPUT y²=11-x] x⁴+2x²y+11-x=49 [Input x²+y=7 into 2x²y] 2x²y = 2x²(7-x²) 2x²y = 14x²-2x⁴ … x⁴+14x²-2x⁴+11-x=49 14x²-x⁴+11-x=49 -38=x-14x²+x⁴ x⁴-14x²+x=-38 [Input x²+y=7 into x⁴-14x²] x⁴-14x² = (7-y)²-14(7-y) x⁴-14x² = 49–14y+y²-118–14y 49–28y+y²-118 -28y+y²-69 [Input x+y²=11 into x] x=11-y² … -28y+y²-69+11-y²=-38 -28y-58=-38 -28y=20 y= - (20/28) ≈ 0.7143 to 5 s.f. [INSERT this into x²+y=7] x²-(20/28)=7 x²=7+(20/28) [7=196/28] x²=(216/28) x=±√(216/28) ≈ ± 2.7775 to 5 s.f. … Therefore, y = -20/28, x = ±√(216/28) |
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