Question
If a + b + c = 18, and a ³ + b ³ + c ³ - 3abc = 54, hen find the value of 5(ab + bc + ca).
Solution
ATQ,
Given, a + b + c = 18
We know that,
So, 54 = 18 × (18²−3(ab + bc + ca))
54 = 18 × (324 − 3(ab + bc + ca))
Divide both sides by 18:
3 = 324 −3(ab + bc + ca)
3(ab + bc + ca) = 321
ab + bc + ca =107
So, required value = 5 × 107= 535
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