Question

x^2+y^2=25 xy=12 then
x=

Answer 1

Value of x will be 4.

Answer 2

Value of x is, ±3 or ±4

Given : The given values are, x²+y² = 25 and xy = 12

To find : The value of x.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the value of x)

Here, we will be using general algebraic formula.

Now,

xy = 12

2 × xy = 2 × 12

2xy = 24

So,

(x²+y²) + 2xy = 25+24

x²+2xy+y² = 49

(x+y)² = 49

x+y = ±7

And,

(x²+y²) - 2xy = 25-24

x²-2xy+y² = 1

(x-y)² = 1

x-y = ±1

Taking, x+y = +7 and x-y = +1

So,

(x+y)-(x-y) = 7-1

2y = 6

y = 3

Now,

xy ÷ y = 12÷3

x = 4

Taking x+y = -7 and x-y = -1

So,

(x+y)-(x-y) = -7-(-1)

2y = -6

y = -3

Now,

xy÷y = 12÷(-3)

x = -4

Taking x+y = +7 and x-y = -1

So,

(x+y)-(x-y) = 7-(-1)

2y = 8

y = 4

Now,

xy ÷ y = 12÷4

x = 3

Taking x+y = -7 and x-y = +1

So,

(x+y)-(x-y) = -7-1

2y = -8

y = -4

Now,

xy ÷ y = 12 ÷ (-4)

x = -3

So, x can be ±3 and ±4

Hence, value of x is ±3 or ±4