What calculation can be used to find the value of p in the equation p^3 =8

Question

asked May 21, 2022 101k views

1 Answer

Salli · Answer 1 · 2022-05-27T10:38:13+0000

Cube Root

${p}^(3) = 8 \\ p = \sqrt[3]{8} \\ p = \sqrt[3]{ 2* 2 * 2} \\ p = 2$

Formula

${p}^(3) - 8 = 0$

Use the following formula.

${x}^(3) - {y}^(3) = (x - y)( {x}^(2) + xy + {y}^(2) )$

$(p - 2)( {p}^(2) + 2p + 4)$

The expression p²+2p+4 has the discriminant less than 0 ( D < 0 ).

Thus, remove the expression and leave only p-2

$p - 2 = 0 \\ p = 2$

Substitution

The most obvious number that multiplies itself three times and equal 8 is 2.

Substitute p = 2

${p}^(3) = 8 \\ {2}^(3) = 8 \\ 2 * 2 * 2 = 8 \\ 8 = 8$

The equation is true, thus 2 is the answer.