If the sum of two numbers is 41 and their product is 400. Then the num

1.	If the sum of two numbers is 41 and their product is 400. Then the numbers are ……………… A) 40, 10 B) 20, 20 C) 25, 16 D) 28, 13
Answer» Correct option is (C) 25, 16 Let the numbers are a and b. Sum of numbers is 41. \(\therefore\) a+b = 41 __________(1) And product of the number is 400. \(\therefore\) ab = 400 __________(2) Now, \((a-b)^2=(a+b)^2-4ab\) \(=41^2-4\times400\) = 1681 - 1600 = 81 \(=9^2\) \(\Rightarrow\) a - b = 9 __________(3) By adding equations (1) & (3), we get (a+b) + (a - b) = 41+9 \(\Rightarrow\) 2a = 50 \(\Rightarrow\) a = \(\frac{50}2\) = 25 \(\therefore\) b = 41 - a (From (1)) = 41 - 25 = 16 Hence, required numbers are 25 and 16. Correct option is C) 25, 16

If the sum of two numbers is 41 and their product is 400. Then the numbers are ……………… A) 40, 10 B) 20, 20 C) 25, 16 D) 28, 13

Answer»

Correct option is (C) 25, 16

Let the numbers are a and b.

Sum of numbers is 41.

\(\therefore\) a+b = 41 __________(1)

And product of the number is 400.

\(\therefore\) ab = 400 __________(2)

Now, \((a-b)^2=(a+b)^2-4ab\)

\(=41^2-4\times400\)

= 1681 - 1600

= 81 \(=9^2\)

\(\Rightarrow\) a - b = 9 __________(3)

By adding equations (1) & (3), we get

(a+b) + (a - b) = 41+9

\(\Rightarrow\) 2a = 50

\(\Rightarrow\) a = \(\frac{50}2\) = 25

\(\therefore\) b = 41 - a (From (1))

= 41 - 25 = 16

Hence, required numbers are 25 and 16.

Correct option is C) 25, 16