Question 5 Quadratic Equations in One Variable Exercise 5.5
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Answer:
Let us consider two numbers as ‘x’ and ‘y’
So according to the question,
1/x – 1/y = 2/15 ….. (i)
It is given that, x + y = 8
So, y = 8 – x … (ii)
Now, substitute the value of y in equation (i), we get
1/x – 1/(8 – x) 2/15
By taking LCM,
[8 – x – x] / x(8 - x) = 2/15
(8 – 2x) / x(8 - x) = 2/15
By cross multiplying,
15(8 – 2x) = 2x(8 - x)
\begin{array}{l} 120-30 x=16 x-2 x^{2} \\ 120-30 x-16 x+2 x^{2}=0 \\ 2 x^{2}-46 x+120=0 \end{array}
Divide by 2, we get
x^{2}-23 x+60=0
let us factorize,
x^{2}-20 x-3 x+60=0
x(x - 20) – 3 (x - 20) = 0
(x - 20) (x - 3) = 0
So,
(x - 20) = 0 or (x - 3) = 0
x = 20 or x = 3
Now,
Sum of two natural numbers, y = 8 – x = 8 – 20 = -12, which is a negative value.
So value of x = 3, y = 8 – x = 8 – 3 = 5
∴ The value of x and y are 3 and 5.
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