Math Question and Answers


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 163437 by cortano1 last updated on 07/Jan/22

Commented by mr W last updated on 07/Jan/22

$m^{3} + n^{3} + p^{3} = {(\sqrt[3]{13})}^{3} + {(\sqrt[3]{53})}^{3} + {(\sqrt[3]{103})}^{3} - 3 \times \frac{1}{3}$ $= 13 + 53 + 103 - 1 = 168$
Commented by cortano1 last updated on 07/Jan/22

$w h a t t h e f o r m u l a ?$
	Answered by mr W last updated on 07/Jan/22

	$s a y m, n, p a r e t h e r o o t s o f e q n .$ $(x - α) (x - β) (x - γ) = δ, i . e .$ $x^{3} - (α + β + γ) x^{2} + (α β + β γ + γ α) x + (α β γ - δ) = 0$ $t h e n w e h a v e$ $m + n + p = α + β + γ$ $m n + n p + p m = α β + β γ + γ α$ $m n p = α β γ - δ$ ${(m + n + p)}^{2} = m^{2} + n^{2} + p^{2} + 2 (m n + n p + p m)$ ${(α + β + γ)}^{2} = α^{2} + β^{2} + γ^{2} + 2 (α β + β γ + γ α)$ $\Rightarrow m^{2} + n^{2} + p^{2} = α^{2} + β^{2} + γ^{2}$ $\Rightarrow (m^{2} + n^{2} + p^{2}) (m + n + p) = (α^{2} + β^{2} + γ^{2}) (α + α + γ)$ $\Rightarrow m^{3} + n^{3} + p^{3} + (m + n + p) (m n + n p + p m) - 3 m n p = α^{3} + β^{3} + β^{3} + (α + β + γ) (α β + β γ + γ α) - 3 α β γ$ $\Rightarrow m^{3} + n^{3} + p^{3} - 3 m n p = α^{3} + β^{3} + β^{3} - 3 α β γ$ $\Rightarrow m^{3} + n^{3} + p^{3} - 3 (α β γ - δ) = α^{3} + β^{3} + β^{3} - 3 α β γ$ $\Rightarrow m^{3} + n^{3} + p^{3} = α^{3} + β^{3} + β^{3} - 3 δ$ $w i t h α = \sqrt[3]{13}, β = \sqrt[3]{53}, γ = \sqrt[3]{103}, δ = \frac{1}{3}$ $\Rightarrow m^{3} + n^{3} + p^{3} = {(\sqrt[3]{13})}^{3} + {(\sqrt[3]{53})}^{3} + {(\sqrt[3]{103})}^{3} - 3 \times \frac{1}{3}$ $\Rightarrow m^{3} + n^{3} + p^{3} = 13 + 53 + 103 - 1 = 168 ◼$
	Commented by Tawa11 last updated on 07/Jan/22

	$Great sir$
	Commented by cortano1 last updated on 07/Jan/22

	$v e r y n i c e$
	Commented by peter frank last updated on 07/Jan/22

	$great$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum