# If (m + n) = 24, and the product of m and n is equal to 15, then find the value of the sum of the squares of the two variables ‘m’ and ‘n’. Also find the value of (m-n)2.

If (m + n) = 24, and the product of m and n is equal to 15, then find the value of the sum of the squares of the two variables ‘m‘ and ‘n’. Also find the value of (m-n)2.

a . 500, 550
b. 516, 546
c. 546, 516
d. 600, 500
e. None of the above

Default Asked on November 21, 2017 in

Thanks for asking question on GMAT Section,

Your question was – If (m + n) = 24, and the product of m and n is equal to 15, then find the value of the sum of the squares of the twovariables ‘m‘ and ‘n’.Alsofind the value of (m-n)2.

Now read this explanation for more clarifications:

According to the data given in the question,
(m + n) = 24…..(i)
m*n = 15……(ii)
We have to find the sum of the squares of the two variables ‘m’ and ‘n’ i.e. m2 + n2
According to the standard mathematical formula,
(m + n)2 = m2 + 2mn + n2……(iii)
∴ (m + n)2 – 2mn = m2 + n2……..(iv)
Substituting the value of m + n from equation (i) and (ii), in equation (iv), we get
(24)2 – 2(15) = m2 + n2
∴ 576 – 30 = m2 + n2
∴ m2 + n2 = 546
We also have to find the value of (m – n)2
Now, according to the standard mathematical formula,
(m – n)2 = m2 – 2mn + n2
∴ (m – n)2 = 546 – 2(15)
∴ (m – n)2 = 546 – 30 = 516
Hence, the correct answer is option c.

Silver Answered on November 21, 2017.