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

User Sola
by
7.6k points

2 Answers

6 votes

Answer:

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

(:

User Lucas Infante
by
8.0k points
5 votes

Answer:

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

User Tiggerae
by
7.8k points