If a + b + c = 5 and a3 + b3 + c3 - 3abc = 185, then the value of ab + bc + ca lies between:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. - 7 and - 3.
If a + b + c = 5 and a3 + b3 + c3 - 3abc = 185
As we know that
a3 + b3 + c3 - 3abc = (a + b + c) * {( a + b + c)2 - 3(ab + bc + ca)}
Put the value in this
185 = 5 * { 52 - 3 * ab + bc + ca}
ab + bc + ca = (25 - 37)/3 = -4
Hence, - 4 lies between -7 and -3