x+√y=7 and √x+y=11 find the value of x and y

### Asked by Mukeshthakur1403 | 8th Jul, 2019, 11:24: PM

Expert Answer:

### x + √y = 7 and √x + y = 11
Consider
√x + y = 11
√x = 11 - y
Squaring on both sides
x = 121 - 22y + y^{2}
Put x = 121 - 22y + y^{2} in the equation x + √y = 7
Let √y = z
we get 121 + z^{4} - 22z^{2} + z = 7
We get factors z = ± 1, ± 2, ± 3, ± 6, ± 19, ± 57, ± 114
z = 3 satisfies the equation.
Now find the value of x and y we get x = 4 and y = 9

^{2}

^{2}in the equation x + √y = 7

^{4}- 22z

^{2}+ z = 7

### Answered by Renu Varma | 9th Jul, 2019, 09:58: AM

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