Question

simplify 1/p+1/q+r / 1/p-1/q+r×(1+q^2+r^2-p^2 / 2qr .​

Answer 1

Answer:

1/(q+r) , 1/(r+p), 1/(p+q) are in AP

it mean common difference always same

so,

1/(r+p) -1/(q+r)=1/(p+q) - 1/(r+p)

(q+r-r-p)/(r+p)(q+r)=(r+p-p-q)/(p+q)(p+r)

(q-p)/(q+r)=(r-q)/(p+q)

use cross multiplication,

q^2-p^2=r^2-q^2

here you see p^2 , q^2 ,r^2 their common difference are same

so, p^2,q^2 ,r^2 are in AP

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Explanation: