If a + b + c = 4, ab + bc + ca = -14 and abc = -18, then the value of √(4a³+4b³+4c³-36) will be:

If a + b + c = 4, ab + bc + ca = -14 and abc = -18, then…

If a + b + c = 4, ab + bc + ca = -14 and abc = -18, then the value of ${\sqrt{4a^3+4b^3+4c^3-36}}$ will be:

Show answer & explanation

Correct answer: D

Explanation

The correct answer is Option 4 i.e. 26.

Given that

a + b + c = 4, ab + bc + ca = -14 and abc = -18

Formula used

a³ + b³ + c³ - 3abc = (a + b + c) [(a + b + c)² - 3(ab + bc + ca)]

By putting the values in this formula

a³ + b³ + c³- 3 * (-18) = 4 * ( 4² - 3* (-14))

a³ + b³ + c³ = 4* 58 - 54 = 178

${\sqrt{4a^3+4b^3+4c^3-36}}$ = ${\sqrt{4(a^3+b^3+c^3)-36}}$ = ${\sqrt{4 * 178-36}}$

= ${\sqrt{676}}$ = 26