Question

If X+y =7 and xy=12 then find X and y

Answer 1

Given :

• x + y = 7
• xy = 12

To find :

• x and y

Solution :

°•° x + y = 7

•°• y = 7 - x ______(1)

xy = 12

Substituting value of y from equation 1

x ( 7 - x) = 12

7x - x² = 12

0 = x² - 7x + 12

Solving the equation by middle term splitting

Middle term splitting :

• Find the factors of constant such that their addition or substraction gives the coefficient of the middle term .
• For example : The factors of 12 ( 3 and 4) when multiplied give 12 and when added give 7 .

0 = x² - ( 3+4)x + 12

0 = x² - 3x - 4x +12

0 = x( x -3) - 4 ( x - 3)

0 = (x -4) ( x -3)

x -4 = 0

x = 4

y = 7 - x = 7-4

y = 3

x - 3 = 0

x = 3

y = 7 - x = 7-3

y = 4

• When x = 4 , y = 3
• When x = 4 , y = 3 When x = 3 , y = 4

Answer 2

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• x + y = 7
• xy = 12

______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• x - y = ??

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

⠀⠀⠀⠀

$\sf{\red{\boxed{\bold{(x+y)^2 - ( x - y)^2 = 4xy}}}}$

⠀⠀⠀⠀

$\sf :\longrightarrow \:{\bold{(7)^2 - ( x - y)^2 = 4\times 12}}$

⠀⠀⠀⠀

$\sf :\longrightarrow \:{\bold{49 - ( x-y)^2 = 48 }}$

⠀⠀⠀⠀

$\sf :\longrightarrow \:{\bold{ ( x - y )^2 = 49 - 48 }}$

⠀⠀⠀⠀

$\sf :\longrightarrow \:{\bold{(x-y)^2 = 1 }}$

⠀⠀⠀⠀

$\sf :\longrightarrow \:{\bold{x-y = \sqrt 1 }}$

⠀⠀⠀⠀

$\sf :\longrightarrow \:{\bold{ x-y = 1 }}$

⠀⠀⠀⠀

Now :-

⠀⠀⠀⠀

x + y = 7 --- ( i )

⠀⠀⠀⠀

x - y = 1 ---- ( ii )

⠀⠀

• Adding eq i and ii

⠀⠀⠀⠀

x + y + x - y = 7 + 1

⠀⠀⠀⠀

2x = 8

⠀⠀

x = 8 / 2

⠀⠀⠀⠀

x = 4

⠀⠀⠀⠀

• putting value of x in eq ( i )

⠀⠀⠀⠀

x + y = 7

⠀⠀⠀⠀

4 + y = 7

⠀⠀⠀⠀

y = 7 - 4

⠀⠀⠀⠀

y = 3

⠀⠀⠀⠀

⠀⠀⠀⠀

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• value of x = 4
• value of y =3