Grade 99 grade maths
Find the value of 1/27 r^3-s^3+125t^3+5rst,when s=r/3 +5t
Find the value of 1/27 r^3-s^3+125t^3+5rst,when s=r/3 +5t
1 Answer
Arun
Dear Preet
s = (r/3) + (5t)
Cubing on both sides,
(s)3 = (r/3 + 5t)3
⇒ s3 = r3/27 + 125 t3 + 3 (r/3)(5t)(r/3 + 5t)
⇒ s3 = r3/27 + 125 t3 + (5rt)(r/3 + 5t)
⇒ s3 = r3/27 + 125 t3 + 5 rst
⇒ r3/27 - s3 + 125 t3 + 5 rst = 0
Therefore, the value of 1/27 r3 - s3 + 125 t3 + 5 rst = 0.
Cubing on both sides,
(s)3 = (r/3 + 5t)3
⇒ s3 = r3/27 + 125 t3 + 3 (r/3)(5t)(r/3 + 5t)
⇒ s3 = r3/27 + 125 t3 + (5rt)(r/3 + 5t)
⇒ s3 = r3/27 + 125 t3 + 5 rst
⇒ r3/27 - s3 + 125 t3 + 5 rst = 0
Therefore, the value of 1/27 r3 - s3 + 125 t3 + 5 rst = 0.
Regards
Arun 9askIITians forum expert)
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