Question

x²-y=11,y²-x=7 then find x ,y​

Answer 1

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)