Grade 11Algebra

If 1/a+1/b+1/c=1/a+b+c then prove that 1/a^n+1/b^n+1/c^n= 1/a^n+b^n+c^n here n is any odd positive integer

Nishita

9 Years agoGrade 11

1 Answer

Harish 423

7 Years ago

$\Bigl( \frac{1}{a} + \frac{1}{b}+ \frac{1}{c}\Bigr) (a+b+c) = 1\\ \\ \implies \sum \frac{1}{a}(b+c)+3=1 \\ \\ \implies \sum bc(b+c)+2abc=0 \\ \\ \implies (b+c)(c+a)(a+b)=0$

Therefore one of (b+c),(c+a),or (a+c) is zero; so we can assume by symmetry , that b = -c

Now for any odd integers n , bⁿ = – cⁿ and therefore

$\Bigl( \frac{1}{a^n} + \frac{1}{b^n}+ \frac{1}{c^n}\Bigr) = \frac{1}{a^n+b^n+c^n}$

What is a binomial expression?

algebra

1 Answer Available

Last Activity: 2 Years ago

Can we divide two vectors? If this is possible then how?

algebra

1 Answer Available

Last Activity: 2 Years ago

How do you write “the product of 18 and q” as an algebraic expression?

algebra

1 Answer Available

Last Activity: 2 Years ago

दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे

algebra

1 Answer Available

Last Activity: 3 Years ago

Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. why HCF and not LCM as “least” keywor dis given?

algebra

1 Answer Available

Last Activity: 3 Years ago

View all Questions

If 1/a+1/b+1/c=1/a+b+c then prove that 1/a^n+1/b^n+1/c^n= 1/a^n+b^n+c^n here n is any odd positive integer

Nishita

1 Answer

Harish 423

Other Related Questions on algebra

What is a binomial expression?

Can we divide two vectors? If this is possible then how?

How do you write “the product of 18 and q” as an algebraic expression?

दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे

Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. why HCF and not LCM as “least” keywor dis given?