Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
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Solution :- Let present age of one friend be x and that of the other 20 – x.
4 years ago age of first friend = x – 4, and that of the other = 20 – x – 4 = 16 – x.
According to question, (x – 4 )(16 – x ) = 48
Or, 16x – x2 – 64 + 4x =48
Or, x2 + 20x – 112 = 0
Or, x2 – 20x + 112 = 0
Here, a = 1, b = – 20, c = 112
D = b2 – 4ac = (– 20 )2 – 4 ×1 × 112 = – 48 < 0.
Hence, the given situation is not possible.
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Let the age of one of the friends be ‘x’.
Age of another friend is (20 – x).
4 years back age of 1st friend is (x – 4)
4 years back age of 2nd friend = (20 – x – 4)
= (16 – x)
Product of their ages is 48.
∴ (x – 4) (16 – x) = 48
16x – x2 – 64 + 4x = 48
-x2 + 20x – 64 = 48
-x2 + 20x – 64 – 48 = 0
-x2 + 20x – 112 = 0
x2 – 20x + 112 = 0
Here, a = 1, b = -20, c = 112
b2 – 4ac = (-20)2 – 4( 1)( 112) = 400 – 448 = – 48
Here, b2 – 4ac = -48 < 0.
∴ It has no real roots.
∴ This situation is not possible.
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