Subjective Type

If $$a + b + c = 0$$, prove that identities $$a^{5} + b^{5} + c^{5} = -5abc (bc + ca + ab)$$.

Solution

SIMILAR QUESTIONS

Polynomials

The sum of values of $$ x $$ satisfying the equation $$ (31+8 \sqrt{15})^{x^{2}-3}+1=(32+8 \sqrt{15})^{x^{2}-3} $$ is

Polynomials

If $$a + b + c = 0$$, prove that identities $$2(a^{4} + b^{4} + c^{4}) = (a^{2} + b^{2} + c^{2})^{2}$$.

Polynomials

If $$a + b + c = 0$$, prove that identities $$(b^{2} c + c^{2}a + a^{2}b - 3abc)(bc^{2} + ca^{2} + ab^{2} - 3abc) = (bc + ca + ab)^{3} + 27a^{2} b^{2} c^{2}$$.

Polynomials

If $$a + b + c = 0$$, prove that identities $$\dfrac {a^{7} + b^{7} + c^{7}}{7} = \dfrac {a^{5} + b^{5} + c^{5}}{5} \cdot \dfrac {a^{2} + b^{2} + c^{2}}{2}$$.

Polynomials

$$(b - c)^{6} + (c - a)^{6} - 3(b - c)^{2}(c - a)^{2} (a - b)^{2} = 2(a^{2} + b^{2} + c^{2} - bc - ca - ab)^{3}$$.

Polynomials

$$(b - c)^{7} + (c - a)^{7} + (a - b)^{7} = 7(b - c)(c - a)(a - b) (a^{2} + b^{2} + c^{2} - bc - ca - ab)^{2}$$.

Polynomials

If $$a + b + c = 0$$, and $$x + y + z = 0$$, show that $$4(ax + by + cz)^{3} - 3(ax + by + cz)(a^{2} + b^{2} + c^{2})(x^{2} + y^{2} + z^{2})\\ - 2(b - c)(c - a)(a - b)(y - z)(z - x)(x - y) = 54\ abcxyz$$.

Polynomials

Show that $$ (97)^3 + ( 14)^3 $$ is divisible by $$111 $$

Polynomials

Factorise the following expression using algebraic identities. $$ a^4 + 6a^2b^2 +9b^4 $$

Polynomials

Factorise the following expression using algebraic identities. $$ x^2 + \dfrac {1}{x^2} + 2 $$

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