If \( x \) is a real number such that \( x^3 = 729 \), then \( x^2 + \sqrt{x} \) equals what?

x 3 = 729 x 2 + x ​ = ? x 3 − 729 = 0 x 3 − 9 3 = 0 ( x − 9 ) ( x 2 + 9 x + 81 ) = 0
x 2 + 9 x + 81 = 0 or x − 9 = 0 Δ = b 2 − 4 a c = 9 2 − 4 ⋅ 1 ⋅ 81 = 81 − 324 = − 243 an d w e kn o w w h e n Δ i s n e g a t i v e , t h eres n o so l u t i o n or x − 9 = 0 x = 9
a 3 − b 3 = ( a − b ) ( a 2 + ab + b 2 ) x 2 + x ​ = 9 2 + 9 ​ = 81 + 3 = 84

Answered by Lilith | 2024-06-10

First, we find the value of 'x.' x 3 = 729 x = 3 729 ​ x=9
x 2 + x ​ 9 2 + 9 ​ 81+3 = 84 x 2 + x ​ =84

Answered by Soham | 2024-06-24

The solution to the equation x 3 = 729 gives us x = 9 . Therefore, calculating x 2 + x ​ yields 84 .
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Answered by Lilith | 2024-09-05