Question

if X square + x = 5 then find X + 3 whole cube + 1 upon X + 3 whole cube

Answer 1

the answer to this question is x= 5/2 i thanks

Answer 2

Concept

An equation that may be written as ax 3 ₊ bx² ₊ cx ₊ d = 0 is referred to as a cubic equation. ax³₊bx²₊cx₊d=0 where a, b, c, and d are all complex numbers and an is a non-zero number. According to the algebraic fundamental theorem, a cubic equation always has three roots, some of which may be equal.

Given

equation, x² ₊ x = 5 .....eq(1)

Find

(x ₊ 3)³ ₊ 1/(x₊3)³ = ?

Solution

(x ₊ 3)³ ₊ 1/(x₊3)³

let m = x ₊ 3

⇒ x = m ₋ 3

m³ ₊ 1/m³

Now substituting x value in eq (1)

(m₋3)² ₊ (m₋3) = 5

m² ₊ 9 ₋ 6m ₊ m ₋ 3 = 5

m² ₋ 5m ₊ 6 = 5

m² ₋ 5m ₊ 1 = 0

m(m ₋ 5) = ₋1

(m ₋ 5) = ₋1/m

(m ₊ 1/m) = 5

now cubing on both sides.

(m ₊ 1/m)³ = 5³

m³ ₊ 1/m³ ₊ 3×m×1/m×(m₊1/m) = 125

m³ ₊ 1/m³ = 125 ₋ 3×5

m³ ₊ 1/m³ = 125 ₋ 15

m³ ₊ 1/m³ = 110

Therefore the value of (x ₊ 3)³ ₊ 1/(x₊3)³ is 110.

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