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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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To show that \[ \frac{1}{1+x^{b-a}+x^{c-a}} + \frac{1}{1+x^{a-b}+x^{c-b}} + \frac{1}{1+x^{b-c}+x^{a-c}} = 1, \] we will simplify the left-hand side step by step. ...
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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

RD SHARMA-EXPONENTS OF REAL NUMBER-All Questions
  1. If x is a positive real number and the exponents are rational number...

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  2. Show that: (i) (x^(a(b-c)))/(x^(b(a-c)))-:((x^b)/(x^a))^c=1, (ii) (...

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

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  4. If a b c=1, show that 1/(1+a+b^(-1))+1/(1+b+c^(-1))+1/(1+c+a^(-1))=1

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  5. Prove that: (a^(-1))/(a^(-1)+b^(-1))+(a^(-1))/(a^(-1)-b^(-1))=(2b^2)/(...

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  6. If a ,\ b ,\ c are distinct positive prime integers such that a^2b^3c^...

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  7. Find the value of x , if 5^(x-3)\xx\ 3^(2x-8)=225

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  8. Solve the following equations: 2^(x-5)=256 (ii) 2^(x+3)=4^(x-1)

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  9. If 9^(x+2)=720+9^x , find the value of (4x)^(1/x)

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  10. Solve the equation for x: 2^(2x+1)=17. 2^x-2^3

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  11. Solve the equation for x 5^(2x+1)=6. 5^x-1

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  12. 3(a^4b^3)^10xx5(a^2b^2)^3

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  13. Simplify that: (2x^(-2)y^3)^3

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  14. Simplify that: ((4\xx\ 10^7)(6\ xx\ 10^(-5)))/(8\ xx\ 10^4)

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  15. Simplify that: (4a b^2\ (-5a b^3))/(10 a^2b^2)

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  16. Simplify that : ((x^2\ y^2)/(a^2b^3))^n

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  17. Simplify that: ((a^(2n-9))^6)/(a^(2n-4))

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  18. If a=3 and b=-2, find the values of: (i)\ a^a+b^b (ii)\ a^b+b^a (iii...

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  19. Prove that: ((x^a)/(x^b))^(a^(2+a b+b^(2)))xx\ ((x^b)/(x^c))^(b^(2+b c...

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  20. Prove that: ((x^a)/(x^b))^c\xx\ ((x^b)/(x^c))^a\ xx\ ((x^c)/(x^a))^b=1

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