The value of xa-b2xb-c2xc-a2-xaxbxc4 is equal to-

The correct option is A 1 We have, #160; (x^a+b)^2(x^b+c)^2(x^c+a)^2/(x^ax^bx^c)^4 = x ^ 2(a+b) · x ^ 2(b+c) · x ^ 2(c+a) / ( x ^ a )^ 4 ·( ...

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Byju's Answer

Standard XII

Mathematics

Arithmetic Progression

The value of ...

Question

The value of $\frac{{(x^{a + b})}^{2} {(x^{b + c})}^{2} {(x^{c + a})}^{2}}{{(x^{a} x^{b} x^{c})}^{4}}$ is equal to:

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Solution

The correct option is A $1$
We have, $\frac{{(x^{a + b})}^{2} {(x^{b + c})}^{2} {(x^{c + a})}^{2}}{{(x^{a} x^{b} x^{c})}^{4}}$
$= \frac{x^{2 (a + b)} \cdot x^{2 (b + c)} \cdot x^{2 (c + a)}}{(x^{a})^{4} \cdot (x^{b})^{4} \cdot (x^{c})^{4}}$
$= \frac{x^{2 a + 2 b} \cdot x^{2 b + 2 c} \cdot x^{2 c + 2 a}}{x^{4 a} \cdot x^{4 b} \cdot x^{4 c}}$
$= \frac{x^{2 a + 2 b + 2 b + 2 c + 2 c + 2 a}}{x^{4 a + 4 b + 4 c}}$
$= \frac{x^{4 a + 4 b + 4 c}}{x^{4 a + 4 b + 4 c}} = 1$

Hence, option A.

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Similar questions

Q. Show that

\frac{{(x^{a + b})}^{2} {(x^{b + c})}^{2} {(x^{c + a})}^{2}}{{(x^{a} x^{b} x^{c})}^{4}} = 1

Prove that :

(i) ${(\frac{x^{a}}{x^{b}})}^{a^{2} + a b + b^{2}} \times {(\frac{x^{b}}{x^{c}})}^{b^{2} + a b + c^{2}} \times {(\frac{x^{c}}{x^{a}})}^{c^{2} + c a + a^{2}} = 1$

(ii) ${(\frac{x^{a}}{x^{b}})}^{c} \times {(\frac{x^{b}}{x^{c}})}^{a} \times {(\frac{x^{c}}{x^{a}})}^{b} = 1$

Q. Simplify :

{(\frac{x^{a}}{x^{b}})}^{a^{2} + a b + b^{2}} \times {(\frac{x^{b}}{x^{c}})}^{b^{2} + b c + c^{2}} \times {(\frac{x^{c}}{x^{a}})}^{c^{2} + c a + a^{2}}

Q. Find the value of the expression:

\frac{(X^{a + b})^{2} \times (X^{b + c})^{2} \times (X^{c + a})^{2}}{(X^{a} X^{b} X^{c})^{4}}

, if

x = 2, a = 1, b = 2, c = 3

Q. The value of

{(\frac{x^{a}}{x^{b}})}^{a^{2} + a b + b^{2}} \cdot {(\frac{x^{b}}{x^{c}})}^{b^{2} + b c + c^{2}} \cdot {(\frac{x^{c}}{x^{a}})}^{c^{2} + c a + b^{2}}

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The value of (xa+b)2(xb+c)2(xc+a)2(xaxbxc)4 is equal to:

The correct option is A 1We have, (xa+b)2(xb+c)2(xc+a)2(xaxbxc)4=x2(a+b)⋅x2(b+c)⋅x2(c+a)(xa)4⋅(xb)4⋅(xc)4=x2a+2b⋅x2b+2c⋅x2c+2ax4a⋅x4b⋅x4c=x2a+2b+2b+2c+2c+2ax4a+4b+4c=x4a+4b+4cx4a+4b+4c=1Hence, option A.

The value of $\frac{{(x^{a + b})}^{2} {(x^{b + c})}^{2} {(x^{c + a})}^{2}}{{(x^{a} x^{b} x^{c})}^{4}}$ is equal to: