1/5 ∝ + 3/4 y - 1/6 ∝ -2/3 y
(only answer)

x=9,y=4

x+y=7+

xy

(i)

x 2 +y 2 =133−xyx

2 +y 2 +xy=133 (ii)

using (a+b) 2=a 2 +b 2 +2ab

(x+y) 2 −xy=133 (iii)

Substituting (i) in (iii), we get

(7+ xy ) 2 −xy=133⇒49+xy+14 xy

−xy=133⇒14 xy

=84⇒ xy

=6⇒xy=36

⇒y= x36

Thus x 2 +( x36 )2 +x. x36=133 (iv)

From (ii), we have x 2 + x 21296

=97⇒x 4 −97x 2 +1296=0⇒x 4 −16x 2 −81x 2

+1296=0⇒x2(x2−16)−81(x2−16)=0⇒(x2−16(x2−81)=0⇒x2=16,81⇒x±4,±9

Negative values are not true for equation (i)

So, x=4,9

Now, y= x36

x=4⇒y= 436

=9x=9⇒y= 936 =4

So, the values of x are 4,9 and corresponding values of y are 9,4

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