Latest maths Aptitude Question SOLUTION: solve for x & y x+sqrt(y)=11 y+sqrt(x)=7 plz give solution

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(#M40030467) MATHS question Keep an EYE

solve for x & y
x+sqrt(y)=11
y+sqrt(x)=7
plz give solution

Asked In maths RAKESH (11 years ago)

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navya  (11 years ago)

x + √y = 11 ----> x = 11 - √y
y + √x = 7
y + √(11 - √y) = 7
√(11 - √y) = 7 - y
11 - √y = 49 - 14y + y^2
-√y = y^2 - 14y + 38
y = y^4 - 28y^3 + 272y^2 - 1064y + 1444
y^4 - 28y^3 + 272y^2 - 1065y + 1444 = 0
(y - 4)(y^3 - 24y^2 + 176y - 361) = 0
y = 4 or three irrational roots

x + √4 = 11
x + 2 = 11
x = 9

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Harsha ludhani  (11 years ago)

1st take 2 no. from 1 which are perfect square .
just think by your aptitude the ans is simply x = 9 and y = 4

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Ruby  (11 years ago)

put x=a^2, y=b^2
eq. will be a^2+b=11 & a+b^2=7
(a^2+b)-(a+b^2)=4
(a^2-b^2)-(a-b)=4
(a-b)(a+b-1)=4
Since the only way to obtain 4 by multiplying is either 2∗2 or 4∗1
first taking 2*2
a-b=2 & a+b=3;
a=5/2 & b=1/2 it doesn't satisfy the given conditions
now taking (a-b)=1 & (a+b-1)=4
a=3,b=2
Hence x=9,y=4

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roushan  (11 years ago)

x=4.4(approx)
y=43.56(approx)
the solution can be obtained by solving the equation simultenous
we get equation as
114+(x)^0.5=x^2+22x this can be solved rigrously or by graph

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Raghavendra V  (11 years ago)

x=9, y=4
just direct calculation.

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