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if p2 + 4q2 +9r2 = 2pq + 6qr + 3pr, then prove that p3 + 8q3 + 27 r3 = 18 pqr

Asked by nisha_vini29 14th September 2015, 12:32 AM
Answered by Expert
Answer:

G i v e n space t h a t space p squared plus 4 q squared plus 9 r squared equals 2 p q plus 6 q r plus 3 p r... left parenthesis 1 right parenthesis W e space k n o w space t h a t space a cubed plus b cubed plus c cubed minus 3 a b c equals open parentheses a plus b plus c close parentheses open parentheses a squared plus b squared plus c squared minus a b minus b c minus c a close parentheses space space space.... left parenthesis 2 right parenthesis space H e r e comma space a equals p comma b equals 2 q space a n d space c equals 3 r. T h e n space u sin g space t h e space a b o v e space i d e n t i t y space left parenthesis 2 right parenthesis space w e space h a v e comma p cubed plus 8 q cubed plus 27 r cubed minus 3 cross times p cross times 2 q cross times 3 r equals open parentheses p plus 2 q plus 3 r close parentheses open parentheses p squared plus 4 q squared plus 9 r squared minus 2 p q minus 6 q r minus 3 p r close parentheses rightwards double arrow p cubed plus 8 q cubed plus 27 r cubed minus 18 p q r equals open parentheses p plus 2 q plus 3 r close parentheses open parentheses p squared plus 4 q squared plus 9 r squared minus 2 p q minus 6 q r minus 3 p r close parentheses rightwards double arrow p cubed plus 8 q cubed plus 27 r cubed minus 18 p q r equals open parentheses p plus 2 q plus 3 r close parentheses cross times 0 space space space open square brackets because p squared plus 4 q squared plus 9 r squared equals 2 p q plus 6 q r plus 3 p r close square brackets rightwards double arrow p cubed plus 8 q cubed plus 27 r cubed minus 18 p q r equals 0 space rightwards double arrow p cubed plus 8 q cubed plus 27 r cubed equals 18 p q r

Answered by Expert 14th September 2015, 5:59 PM
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