If (x2+y2+z2)=(xy+yz+zx), what is the value of x3+y3+z3?

Sail E0 Webinar

Question

If $(x^{2} + y^{2} + z^{2}) = (x y + y z + z x)$ , $what is the value of x^{3} + y^{3} + z^{3}$ ?

Options:

A .

3 x y z

B .

- 3 x y z

C .

2 x y z

D .

- 2 x y z

Answer: Option A
:
A

We know that
$x^{3} + y^{3} + z^{3} - 3 x y z = (x + y + z) (x^{2} + y^{2} + z^{2} - x y - y z - z x) - - - (1)$
According to question, $(x^{2} + y^{2} + z^{2}) = (x y + y z + z x)$ .
$∴$ RHS will be zero in equation (1)
So, $x^{3} + y^{3} + z^{3} = 3 x y z$

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. If (x−1) is a factor of ax3−bx2+cx, what is the value of a3−b3+c3? ....

Question 2. If (x2−y2)=18 and (x−y)=3, find the value of 16x2y2. ....

Question 3. If xg+1xa is a polynomial in one variable and if it is given that g = a, for what value of 'a' is this a polynomial? ....a, for what value of 'a' is this a polynomial? ___

Question 4. In a2x2+ax, if 'a' is constant and 'x' is a variable, this expression would become a polynomial in ___ variable(s). (W....become a polynomial in ___ variable(s). (Write in words)

Question 5. p(x)=x3+8x2−7x+12 and g(x)=x−1. If p(x) is divided by g(x), it gives q(x) and r(x) as quotient and remai....of q(x) and b is the degree of r(x), (a−b)=?.

Question 6. Factorize : x2−7x+12 ....

Question 7. The value of (2x−3y)3+(x+3y)3+3(2x−3y)2(x+3y)+3(2x−3y)(x+3y)2= ....

Question 8. Degree of a constant polynomial is _____. ....

Question 9. If x+x−1=11, evaluate x2+x−2. ....

Question 10. The polynomial ax3+bx2+x–6 has (x+2) as a factor and leaves a remainder 4 when divided by (x–2). Find a ....remainder 4 when divided by (x–2). Find a and b.

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

GPOE / GPA Combined 1 Free Mock Test SAIL JO E-0 2024

Chapter 3.1 : INTRODUCTION Chapter 3 : Sinter Plant SAIL E0 - GPOE/GPA 2024

Chapter 2.3 : COAL HANDLING PLANT - Set 1 Chapter 2 : Coke Ovens and Coal Chemicals SAIL E0 - GPOE/GPA 2024

Chapter 1.1 : INTRODUCTION Chapter 1 : Raw Material Handling Plant SAIL E0 - GPOE/GPA 2024

DSP Combined 1 Free Revision Test SAIL JO E-0