Question : If a, b, c are real and $a^{2} + b^{2} + c^{2} = 2 (a - b - c) - 3,$ then the value of $2 a - 3 b + 4 c$ is:
Option 1: –1
Option 2: 0
Option 3: 1
Option 4: 2

Question

Question : If $a + b + c = 0$ and $a^{2} + b^{2} + c^{2} = 40$ , then what is the value of $a b + b c + c a$ ?
Option 1: –30
Option 2: –20
Option 3: –25
Option 4: –40

24 Views

Answer 1

Correct Answer: 1

Solution : Given: $a^{2} + b^{2} + c^{2} = 2 (a - b - c) - 3$ .
We can simplify the above equation as follows:
⇒ $a^{2} + b^{2} + c^{2} = 2 a - 2 b - 2 c - 3$
⇒ $a^{2} - 2 a + 1 + b^{2} + 2 b + 1 + c^{2} + 2 c + 1 = 0$
⇒ $(a - 1)^{2} + (b + 1)^{2} + (c + 1)^{2} = 0$
$∴ a = 1, b = - 1, c = - 1$
Putting the values of $a, b, c$ in $2 a - 3 b + 4 c$ , we get:
$2 + 3 - 4 = 1$
Hence, the correct answer is 1.

Exams

Colleges

Predictors

Resources

Quick links

Exams

Colleges & Courses

Predictors

Resources

Exams

Colleges

Predictors & E-Books

Resources

Engineering Preparation

Medical Preparation

Law Preparation

MBA Preparation

Exams

Colleges

Resources

Exams

Colleges

Predictors & Articles

Resources

Exams

Colleges

Predictors

Resources

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges

Resources

Quick Links

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Resources

Diploma Colleges

Exams

Colleges

Resources

Exams

Resources

Top Courses & Careers

Colleges

Exams

Upcoming Events

Resources

Other Exams

Exams

Colleges

Top Countries

Resources

Exams

Top Schools

Products & Resources

NCERT Study Material

Question : If a, b, c are real and a2+b2+c2=2(a−b−c)−3, then the value of 2a−3b+4c is:Option 1: –1Option 2: 0Option 3: 1Option 4: 2

Related Questions

Know More about

Upcoming Exams

Trending Articles around SSC CHSL

Download the Careers360 App on your Android phone

Sign In/Sign Up

Question : If a, b, c are real and $a^{2} + b^{2} + c^{2} = 2 (a - b - c) - 3,$ then the value of $2 a - 3 b + 4 c$ is:
Option 1: –1
Option 2: 0
Option 3: 1
Option 4: 2