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Solve for n: D/A×{1−((P×((((1+i)^n ×i)/((1+i)^n −1))))/((P×((((1+i)^r ×i)/((1+i)^r −1))))−(R/i)×[((1/n)+i)×((((1+i)^r ×i)/((1+i)^r −1)))−((1/n)+i)×((((1+i)^n ×i)/((1+i)^n −1)))]))}−1=0

$S o l v e f o r n : D / A \times {1 - \frac{P \times (\frac{{(1 + i)}^{n} \times i}{{(1 + i)}^{n} - 1})}{(P \times (\frac{{(1 + i)}^{r} \times i}{{(1 + i)}^{r} - 1})) - \frac{R}{i} \times [(\frac{1}{n} + i) \times (\frac{{(1 + i)}^{r} \times i}{{(1 + i)}^{r} - 1}) - (\frac{1}{n} + i) \times (\frac{{(1 + i)}^{n} \times i}{{(1 + i)}^{n} - 1})]}} - 1 = 0$

Question Number 61495 Answers: 1 Comments: 7

Question Number 61490 Answers: 0 Comments: 10

(√(a−(√(a+x))))+(√(a+(√(a−x))))=2x this is the solution Sir Aifour and me found trivial solution a=x=0 a, x ∈R x=((√2)/8)(r+(√(r^2 +4)))(√(2(4a−1)−r^2 −r(√(r^2 +4)))) with r=−2(√((4a−3)/3))sin ((1/3)arcsin ((3(√3))/((4a−3)^(3/2) ))) no solution for a<a_0 with a_0 ≈1.509830340886

$\sqrt{a - \sqrt{a + x}} + \sqrt{a + \sqrt{a - x}} = 2 x$ $this is the solution Sir Aifour and me found$ $trivial solution a = x = 0$ $a, x \in R$ $x = \frac{\sqrt{2}}{8} (r + \sqrt{r^{2} + 4}) \sqrt{2 (4 a - 1) - r^{2} - r \sqrt{r^{2} + 4}}$ $with$ $r = - 2 \sqrt{\frac{4 a - 3}{3}} \sin (\frac{1}{3} \arcsin \frac{3 \sqrt{3}}{{(4 a - 3)}^{\frac{3}{2}}})$ $no solution for a < a_{0} with a_{0} \approx 1.509830340886$

Question Number 61470 Answers: 1 Comments: 0

Is there any other solution besides {x=a,y=b} or {x=b,y=a} of the following system of equations x+y=a+b ∧ x^7 +y^7 =a^7 +b^7 ?

$Is there any other solution besides$ ${x = a, y = b} or {x = b, y = a} of the$ $following system of equations$ $x + y = a + b \land x^{7} + y^{7} = a^{7} + b^{7} ?$

Question Number 61343 Answers: 1 Comments: 0

Question Number 61320 Answers: 1 Comments: 0

solve for x: x^4 −x=12

$solve for x :$ $x^{4} - x = 12$

Question Number 61272 Answers: 0 Comments: 0

Question Number 61273 Answers: 2 Comments: 2

Suppose α ,β,γ,δ are real numbers such that α+β+γ+δ = α^7 +β^7 +γ^7 +δ^7 =0 Prove that α(α+β)(α+γ)(α+δ)=0

$S u p p o s e α, β, γ, δ a r e r e a l n u m b e r s$ $s u c h t h a t α + β + γ + δ = α^{7} + β^{7} + γ^{7} + δ^{7} = 0$ $P r o v e t h a t α (α + β) (α + γ) (α + δ) = 0$

Question Number 61269 Answers: 3 Comments: 0

Let p(x) be a quadratic polynomial such that for distinct α and β , p(α) = α and p(β) =β prove that α and β are roots of p[p(x)]−x=0 Find the remaining roots .

$L e t p (x) b e a q u a d r a t i c p o l y n o m i a l s u c h$ $t h a t f o r d i s t i n c t α a n d β,$ $p (α) = α a n d p (β) = β$ $p r o v e t h a t α a n d β a r e r o o t s o f p [p (x)] - x = 0$ $F i n d t h e r e m a i n i n g r o o t s .$