Question

If a + b = 20 and ab = 75, find the value of a + b?​

Answer 1

a=5 or a=15, b=15 or b=5

Explanation:

b=20-a

a(20-a)=75

20a-
`a^(2)` -75=0

-
`a^(2)`+20a-75=0

`a^(2)`-20a+75=0

(a-5)(a-15)=0

a-5=0 or a-15=0

a=5 or a=15

b=15 or b=5

(:

Answer 2

Explanation:

a + b = 20

Sum of roots = 20

ab = 75

Product of roots = 75

x² - (a +b) x + ab = 0

x² - 20x + 75 = 0

Sum = coefficient of x = -20

Product = 75

Factors = 15 , 5 {15*5 = 75 & 15 +5 = 20}

x² - 15x - 5x + 75 = 0 {Rewrite the middle term}

x(x - 15) - 5(x - 15) = 0

(x - 15) (x - 5)=0

x - 15 = 0 ; x -5 = 0

x = 15 ; x = 5

a = 15 ; b= 5