Question 30041: Please help me solve this equation:
The sum of two numbers is 6 & their product is 4. Find the larger of the two numbers.
Thanks:) Answer by sdmmadam@yahoo.com(530) (Show Source):
You can put this solution on YOUR website! The sum of two numbers is 6 & their product is 4.
Let the two numbers be A and B say with A > B
The sum of two numbers is 6
A+B =6 ----(1)
their product is 4
AB = 4 ----(2)
We have by formula (A-B)^2 = (A+B)^2-4AB
Therefore (A-B)^2 = 6^2-4X4 = 36-16 = 20
(A-B)^2 = 20
Therefore taking the positive sqrt (since A > B, we have (A-B) > 0)
(A-B) = sqrt(20)
That is A - B = 2sqrt of 5 ----(3)
And A+B = 6 ----(1)
(3)+(1) implies
(A+A) = 2(rt5)+6
2A = 2(rt5)+6
dividing by 2
Therefore A = [sqrt(5)+3]
Putting A = [sqrt(5)+3] in (1)
B = 6-A
B =6 -[sqrt(5)+3] = 6 - sqrt(5)-3 = (6-3)-sqrt(5) = 3-sqrt(5)
Answer: A = [3+ sqrt of 5] and B = [3 -sqrt of 5]
Verification: AB = [3+ sqrt of 5]X[3 -sqrt of 5]
=3^2- (rt5)^2 = 9-5 = 4 which is correct
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