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Solve an equation involving the sum of two cubes.
MATHEMATICS · Multi-part · CBSE · Mathematics · Polynomials · Polynomials
Problem
Solve an equation involving the sum of two cubes. (i) Simplify
(
x
+
1
)
3
+
(
x
−
1
)
3
(x + 1)^3 + (x - 1)^3
(
x
+
1
)
3
+
(
x
−
1
)
3
. (ii) Using the result of part (i), solve
(
x
+
1
)
3
+
(
x
−
1
)
3
=
100
x
(x + 1)^3 + (x - 1)^3 = 100x
(
x
+
1
)
3
+
(
x
−
1
)
3
=
100
x
for real
x
x
x
. (iii) Verify each root by direct substitution in the original equation.
Related theory
Solving Quadratic Equations
Quadratic Equations
Algebraic Identities
Polynomials
Algebra
Algebraic expansions
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