Question : If $x^{2} + y^{2} + z^{2} = x y + y z + z x$ , then the value of $\frac{3 x^{4} + 7 y^{4} + 5 z^{4}}{5 x^{2} y^{2} + 7 y^{2} z^{2} + 3 z^{2} x^{2}}$ is:
Option 1: 2
Option 2: 1
Option 3: 0
Option 4: –1

Question

Question : If $x + y + z = 0$ , then the value of $\frac{x^{2}}{y z} + \frac{y^{2}}{z x} + \frac{z^{2}}{x y}$ is:

8 Views

Answer 1

Correct Answer: 1

Solution : Given: $x^{2} + y^{2} + z^{2} = x y + y z + z x$
⇒ $x^{2} + y^{2} + z^{2} - x y - y z - z x = 0$
⇒ $\frac{1}{2} [(x - y)^{2} + (y - z)^{2} + (z - x)^{2}] = 0$
So, $(x - y) = 0$ , $(y - z) = 0$ , $(z - x) = 0$
So, $x = y = z$
Putting this value in the given condition, we have:
$\frac{3 x^{4} + 7 y^{4} + 5 z^{4}}{5 x^{2} y^{2} + 7 y^{2} z^{2} + 3 z^{2} x^{2}} = \frac{15 x^{4}}{15 x^{4}} = 1$
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

Online Courses

Products

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

Student Visas

Exams

Top Schools

Products & Resources

NCERT Study Material

Question : If x2+y2+z2=xy+yz+zx, then the value of 3x4+7y4+5z45x2y2+7y2z2+3z2x2 is:Option 1: 2Option 2: 1Option 3: 0Option 4: –1

Related Questions

Know More about

Upcoming Exams

Trending Articles around SSC CGL

Download the Careers360 App on your Android phone

Sign In/Sign Up

Question : If $x^{2} + y^{2} + z^{2} = x y + y z + z x$ , then the value of $\frac{3 x^{4} + 7 y^{4} + 5 z^{4}}{5 x^{2} y^{2} + 7 y^{2} z^{2} + 3 z^{2} x^{2}}$ is:
Option 1: 2
Option 2: 1
Option 3: 0
Option 4: –1