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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

Course
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.

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#### 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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