Question

if xy=6 and x²+y²=5 then the value of (x+y)² is​

Answer 1

Answer:

We are given that

xy = 2 ……………….(1)

and x^2 + y^2 = 5 …………………..(2)

Since we know that

(x+y)^2 = x^2 + y^2 + 2xy

From (1) and (2) substituting the values, we get

(x+y)^2 = 5 + 2*2

(x+y)^2 = 9

therefore x+y = 3 or -3

Taking x+y = 3 …………….(3)

Solving (1) and (3)

we get the quadratic equation

x^2 - 3x +2 = 0

Solving it we get x = 2 ,1

putting in (1)

we get y = 1, 2 respectively

Therefore x=1 and y=2 or x=2 and y=1

Now considering x + y = -3 …………..(4)

Solving (1) and(4) we get the quadratic equation as

x^2 + 3x +2 = 0

Solving it we get

x = -2,-1

putting these values of x in (1) we get

y = -1, -2 respectively.

Therefore x=-1, y= -2 or x= -2, y=-1

Hence we get overall 4 solutions for x and y.

x=1, y= 2.

x= 2, y= 1.

x = -1, y= -2.

x= -2, y= -1.

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