Question 683830: one positive number is 4 more than twice another.. if their product is 448 find the numbers
Answer by Jolliano(16)   (Show Source):
You can put this solution on YOUR website! Let x be the greater number and y the smaller one.
From the 1st line,
x > 2y by 4.
That gives us the equation
x = 2y + 4.....(1)
From the second line,
x*y = 448
xy = 448
Substitute eqn(1) into (2)
xy = 448
:-(2y +4)y = 448
Expanding the bracket,
2y^2 + 4y = 448
Solving this equation using completing the square method.
Divide through by 2,
y^2 + 2y = 224.
y^2 + 2y + (1^2) = 224 +(1^2)
y^2 + 2y + 1 = 224 + 1
Factorising the L.H.S,
(y + 1)^2 = 225
Find the root of both sides,
(y + 1) = ±√ 225
y + 1 = ± 15
Taking positive root,
y + 1 = 15
y = 15 - 1
y =14
Then
x = 2y + 4
x = 2(14) + 4
x = 28 + 4
x = 32.
Taking negative root,
y + 1 = -15
y = -15 - 1
y = -16
Then
x = 2y + 4
x = 2(-16) + 4
x = -32 + 4
x = -28
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