Question

23. यदि दो धनात्मक संख्याओं का योग 25 एवं उनका गुणनफल 144 हो, तो उन संख्याओं का
अंतर होगा-
(i) 3 (ii) 5 (iii) 7 (iv) 11​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

If the Sum of two positive numbers is 25 and product of them is 144 , then their difference is

(i) 3

(ii) 5

(iii) 7

(iv) 11

EVALUATION

Let the two numbers are x and y

Now it is given that the Sum of two positive numbers is 25 and product of them is 144

So by the given condition

x + y = 25 and xy = 144

Now

$\sf{ {(x - y)}^{2} = {(x + y)}^{2} - 4xy }$

$\sf{ \implies \: {(x - y)}^{2} = {(25)}^{2} - 4 \times 144 }$

$\sf{ \implies \: {(x - y)}^{2} = 625 - 576 }$

$\sf{ \implies \: {(x - y)}^{2} = 49}$

$\sf{ \implies \:x - y = 7 }$

FINAL ANSWER

Hence the correct option is (iii) 7

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