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If a and B Are Different Positive Primes Such that `(A+B)^-1(A^-1+B^-1)=A^Xb^Y,` Find X + Y + 2. - Mathematics

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ConceptLaws of Exponents for Real Numbers

Question

If a and b are different positive primes such that

`(a+b)^-1(a^-1+b^-1)=a^xb^y,` find x + y + 2.

Solution

`(a+b)^-1(a^-1+b^-1)=a^xb^y`

`rArr1/(a+b)(1/a+1/b)=a^xb^y`

`rArr1/(a+b)((a+b)/(ab))=a^xb^y`

`rArr(1/(ab))=a^xb^y`

`rArr(ab)^-1=a^xb6y`

`rArra^-1b^-1=a^xb^y`

⇒ x = -1 and y = -1

Therefore, the value of x + y + 2 is -1 - 1 + 2 = 0.

  Is there an error in this question or solution?

APPEARS IN

 RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 2: Exponents of Real Numbers
Ex. 2.2 | Q: 18.2 | Page no. 26

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Solution If a and B Are Different Positive Primes Such that `(A+B)^-1(A^-1+B^-1)=A^Xb^Y,` Find X + Y + 2. Concept: Laws of Exponents for Real Numbers.
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