Ex 4.3, 4
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.
Let the Present age of 1st friend = x
Given that
Sum of ages of friends is 20 years
Thus,
Present age of 1st friend + Present age of 2nd friend = 20
x + Present age of 2nd friend = 20
Present age of 2nd friend = 20 – x
Four years ago
Age of 1st friend = x – 4
Age of 2nd friend = (20 – x) – 4 = 16 – x
Product of their ages 4 years ago was 48
(x – 4) (16 – x) = 48
Four years ago
Age of 1st friend = x – 4
Age of 2nd friend = (20 – x) – 4 = 16 – x
Product of their ages 4 years ago was 48
(x – 4) (16 – x) = 48
x (16 – x) – 4 (16 – x) = 48
16x – x2 – 64 + 4x = 48
16x – x2 – 64 – 14x – 48 = 0
– x2 + 16x + 4x – 64 – 48 = 0
– x2 + 20x – 112 = 0
x2 – 20x + 112 = 0
Comparing the equation with ax2 + bx + c
a = 1, b = –20, c = 112
We know that
D = b2 – 4ac
D = (–20)2 – (4 × 𝟏 × 𝟏𝟏𝟐)
D = 400 – 448
D = –48
Since D < 0
The equation has no real roots
Hence, the given situation is not possible

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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