If the sum of the squares of three numbers is 138, and the sum of the products of these numbers taken two at a time is 131, what is the sum of the three numbers?

Problems on Numbers MCQs for PPSC, FPSC, NTS, and Pakistan government job tests. Select an option below, then read the explanation.

Browse all Problems on Numbers MCQs →

PPSCFPSCNTSPakistan govt jobs

Subject: Problems on Numbersmathematics-mcqs › problems-on-numbers
Published: 9 Oct 2019
Last updated: 28 May 2026

Browse all Problems on Numbers MCQs →

Explanation

Let the three numbers be x, y, and z. Given that x² + y² + z² = 138 and xy + yz + zx = 131. Using the identity (x + y + z)² = x² + y² + z² + 2(xy + yz + zx), we get (x + y + z)² = 138 + 2(131) = 138 + 262 = 400. Therefore, x + y + z = √400 = 20.

Practice related questions from the same subject.

1.One number is 5 greater than another number. If their total is 19, what is the smaller number?
2.Ahmed buys a watch priced at Rs 600 and is required to pay a 15% sales tax. What is the total amount he has to pay?
3.Identify two numbers whose sum equals 28 and whose difference is 4.
4.A two-digit number's digits are swapped to form a new number that is 18 greater than the original. If the sum of the digits is 8, what is the original number?
5.Find the two-digit number whose digits multiply to 8, and when 18 is added to the number, the digits switch places.
6.Identify the number that, when multiplied by 15, results in a value that is 196 greater than the original number.
7.Three numbers are in the ratio 3 : 4 : 6, and their product equals 1944. What is the value of the largest number?
8.A number added to its square equals 182. What is the value of this number?

← Back to Mathematics Mcqs

If the sum of the squares of three numbers is 138, and the sum of the products of these numbers taken two at a time is 131, what is the sum of the three numbers?

Explanation

More Problems on Numbers MCQs