If a - b = 4, b - c = 6 and a - c = 10, then the value of a^2 + b^2 + c^2 - ab - bc - ca is: Option 1: 52 Option 2: 62 Option 3: 71 Option 4: 76

Answer: 76. Solution: Use the identity a^2+b^2+c^2-ab-bc-ca = 1/2[(a-b)^2+(b-c)^2+(c-a)^2]. Substituting: 1/2[4^2 + 6^2 + 10^2] = 1/2(16+36+100) = 152/2 = 76.

Quantitative Reasoning

Number System

Medium

If a - b = 4, b - c = 6 and a - c = 10, then the value of $a^2 + b^2 + c^2 - ab - bc - ca$ is:

✅ Correct Option: 4

Use the identity $a^2+b^2+c^2-ab-bc-ca = \frac{1}{2}\left[(a-b)^2+(b-c)^2+(c-a)^2\right]$ .

Substituting: $\frac{1}{2}\left[4^2 + 6^2 + 10^2\right] = \frac{1}{2}(16+36+100) = \frac{152}{2} = 76$ .

2024

The difference of the greatest and the smallest of the fractions $\frac{1}{2}$ , $\frac{8}{11}$ , $\frac{7}{8}$ , $\frac{7}{9}$ , $\frac{5}{6}$ is:

2026: 14 May Shift 1

Which one is correct

A. $\sqrt{3}$ is irrational

B. Sum of two irrational number is always irrational

C. $\sqrt{p}$ , where $p$ is prime, is irrational

D. Every composite number can be expressed as a product of primes

Choose the correct answer from the options given below:

2022: 26 Aug Shift 1

The value of $\left(\frac{8}{125}\right)^{\frac{-4}{3}}$ is __________

2022: 23 Aug Shift 1

The value of $\sqrt{.01} \times \sqrt[3]{.027} - 0.3$ is

2025: 20 May Shift 1

How many perfect squares lie between 120 and 300?

2025: 3 June Shift 2

Which one of the following is/are correct?

(A) Every irrational number is a real number.

(B) Every real number is an irrational number.

(D) The product or quotient of a non-zero rational number with an irrational number is an irrational number.

Choose the correct answer from the options given below:

If a - b = 4, b - c = 6 and a - c = 10, then the value of a2+b2+c2−ab−bc−caa^2 + b^2 + c^2 - ab - bc - caa2+b2+c2−ab−bc−ca is:

Solution

Related questions:

Keyboard Shortcuts

CUET General Test Past Year Questions (Topic-Wise)

If a - b = 4, b - c = 6 and a - c = 10, then the value of $a^2 + b^2 + c^2 - ab - bc - ca$ is: