Question

if a + b =15 and ab =50.find the value of a^2 + b^2​

Answer 1

Step-by-step explanation:

given: a+b= 15.................(1)

ab= 50...................(2)

need to solve: a^2+b^2

equation (1) ; by squaring on both sides....

so, (a+b)^2= (15)^2

we know that: (a+b)^2= a^2+b^2+2ab

so, a^2+b^2+2ab= 225.................(3)

equation (4) multiply both sides by 4

so, 4(ab=50)

4ab= 200...............(4)

so by subtracting equations (3)-(4)

a^2+b^2+2ab-4ab= 225-200

so, a^2+b^2-2ab= 25

a^2+b^2-2ab= (a-b)^2

so, (a-b)^2= 25

a-b= √25=5

so, a-b= 5..................(5)

adding equations (1)+(5)

a+b+a-b= 15+5

by cancelling b..........

a+a= 20

2a=20

a=20/2=10

so, a=10

by , substituting in equation (1)

10+b=15

so, b=5

a=10, b=5

so, a^2+b^2= (10)^2+(5)^2= 100+25= 125

so, a^2+b^2= 125