Question

If x+y= 5 & xy= 10 find the value of x^2 + y^2

Answer 1

Answer:

Given: x+y = 5 and xy = 10

Find: x and y

soln:

Consider x = 5-y

xy = 10

(5-y)y = 10

5y-y^2 = 10

0 = y^2 -5y +10

The roots can be finded by the equation

-b +- Sqrt(b^2 -4ac)/2a

5 + Sqrt((-5)^2 -4*1*10)/2*1

5 + Sqrt(25–40)/2

5 + Sqrt(-15)/2

5 + (-3.87)/2

5 + -1.935

3.065

5 - Sqrt((-5)^2 -4*1*10)/2*1

5 - Sqrt(25–40)/2

5 - Sqrt(-15)/2

5 - (-3.87)/2

5 - (-5 + Sqrt((-5)^2 -4*1*10)/2*1

5 + Sqrt(25–40)/2

5 + Sqrt(-15)/2

5 + (-3.87)/2

5 + -1.935)

5 + 1.935

6.935

y = 6.935 , 3.065

xy = 10 [Given]

x = 5-y

x = 5–6.935 = - 1.935

x = 5–3.065 = 1.935

Hence x= - 1.935, 1.935; y= 6.935 , 3.065 : Final Answer

Answer 2

Step-by-step explanation:

x+y=5

taking square on both side

(x+y)²=5²

open the square

x²+y²+2xy=25

since xy=10

x²+y²+2(10)=25

x²+y²+20=25

x²+y²=25-20

x²+y²=5