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Show that: 1/(1+x^(b-a)+x^(c-a))+1/(1+x^...

Show that: `1/(1+x^(b-a)+x^(c-a))+1/(1+x^(a-b)+\ x^(c-b))+1/(1+x^(b-c)+\ x^(a-c))=1`

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The correct Answer is:
1 = RHS.
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(1)/(1+x^(b-a)+x^(c-a))+(1)/(1+x^(a-b)+x^(c-b))+(1)/(1+x^(a-c)+x^(b-c))

Differentiate (1)/(1+x^(b-a)+x^(c-a))+(1)/(1+x^(a-b)+x^(c-b))+(1)/(1+x^(a-c)+x^(b-c)) w.r.t. to x.

(1)/(1+x^(a-b)+x^(a-c))+(1)/(1+x^(b-c)+x^(b-a))+(1)/(1+x^(c-a)+x^(c-b))=1

If y = (1)/(1 + x^(a - b) + x^(c - b)) + (1)/(1 + x^(b-c) + x^(a - c)) + (1)/(1 + x^(b - a) + x^(c - a)) then find (dy)/(dx) at e^(a^(b^(c )))

(1)/(x^(b)+x^(-c)+1)+(1)/(x^(c)+x^(-a)+1)+(1)/(x^(a)+x^(-b)+1)

Show that: (x^(a(b-c)))/(x^(b(a-c)))-:((x^(b))/(x^(a)))^(c)=1((x^(a+b))(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))=1

Assuming that x is a positive real number and a,b,c are rational numbers,show that: ((x^(a))/(x^(b)))^((1)/(ab))((x^(b))/(x^(c)))^((1)/(bc))((x^(c))/(x^(a)))^((1)/(ac))=1

MTG IIT JEE FOUNDATION-EXPONENTS AND POWERS-Solved Examples
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  2. Simplify: (i) (2 ^(-1) xx 5 ^(-1)) ^(-1) div 4 ^(-1) (ii) (4 ^(-1)...

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  11. Simplify (i) <img class="eeimg trnoresize" alt="\left\{ {{{\lef...

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  14. Simplify : ((3)/(7))^(-2) xx ((7)/(6))^(-3)

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  16. Write the following numbers in standard form. 0.000007

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  18. Write the following numbers in standard form: 0. 4579 (ii) 0. 000007 ...

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  19. Write the following numbers in standard form: 0. 4579 (ii) 0. 000007 ...

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  20. Write the following numbers in standard form: 0. 4579 (ii) 0. 000007 ...

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