If $1 over straight p space plus space 1 over straight q space equals space fraction numerator 1 over denominator straight p plus straight q end fraction comma$ then the value of p³ - q³

p - q

pq

1

1

1 over straight p space plus space 1 over straight q space equals space fraction numerator 1 over denominator straight p plus straight q end fraction

rightwards double arrow space space space fraction numerator straight p plus straight q over denominator pq end fraction space equals space fraction numerator 1 over denominator straight p plus straight q end fraction

rightwards double arrow space space left parenthesis straight p plus straight q right parenthesis squared space equals space pq rightwards double arrow space space straight p squared plus straight q squared plus 2 pq space equals space pq rightwards double arrow space space straight p squared plus straight q squared plus pq space equals space 0

straight p cubed minus straight q cubed space equals space left parenthesis straight p minus straight q right parenthesis thin space left parenthesis straight p squared plus straight q squared plus pq right parenthesis space space space space space space space space space equals space left parenthesis straight p minus straight q right parenthesis space cross times space 0 space equals space 0

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Algebra

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