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AlgebraQuestion and Answers: Page 269

Question Number 84002 Answers: 0 Comments: 0

((sin(x))/(√(2sin^2 (x)+cos^2 (x)))) +(1/(√2))=csc(x)(√(2sin^2 (x)+cos^2 (x))) show that x={(π/2)+2πn} and x={cos^(−1) ((√3))−π+2πn} and x={−cos^(−1) ((√3))+2πn}

$\frac{s i n (x)}{\sqrt{2 {s i n}^{2} (x) + {c o s}^{2} (x)}} + \frac{1}{\sqrt{2}} = c s c (x) \sqrt{2 {s i n}^{2} (x) + {c o s}^{2} (x)}$ $s h o w t h a t$ $x = {\frac{π}{2} + 2 π n} a n d x = {{c o s}^{- 1} (\sqrt{3}) - π + 2 π n}$ $a n d x = {- {c o s}^{- 1} (\sqrt{3}) + 2 π n}$

Question Number 84005 Answers: 2 Comments: 4

find atleast 7 solutions of the equation. 900x+7689y=109876 CAN ANYONE SOLVE THIS now lets find 7 integral solutions

$f i n d a t l e a s t 7 s o l u t i o n s$ $o f t h e e q u a t i o n .$ $900 x + 7689 y = 109876$ $C A N A N Y O N E S O L V E$ $T H I S$ $n o w l e t s f i n d 7 i n t e g r a l$ $s o l u t i o n s$

Question Number 83941 Answers: 1 Comments: 0

If ((2 ))^(1/3) + (4)^(1/(3 )) + ((8 ))^(1/(3 )) = x then x^3 −6x^2 +6x+6 = ?

$If \sqrt[3]{2} + \sqrt[3]{4} + \sqrt[3]{8} = x$ $then x^{3} - {6 x}^{2} + 6 x + 6 = ?$

Question Number 83931 Answers: 1 Comments: 1

(1/(((√1)+(√2))((1)^(1/(4 )) +(2)^(1/(4 )) ))) + (1/(((√2)+(√3))((2)^(1/( 4)) +(3)^(1/(4 )) ))) + (1/(((√3)+(√4))((3)^(1/(4 )) +(4)^(1/(4 )) ))) + ... + (1/(((√(255))+(√(256)))(((255))^(1/(4 )) +((256))^(1/(4 )) ))) = ...

$\frac{1}{(\sqrt{1} + \sqrt{2}) (\sqrt[4]{1} + \sqrt[4]{2})} + \frac{1}{(\sqrt{2} + \sqrt{3}) (\sqrt[4]{2} + \sqrt[4]{3})} +$ $\frac{1}{(\sqrt{3} + \sqrt{4}) (\sqrt[4]{3} + \sqrt[4]{4})} + . . . + \frac{1}{(\sqrt{255} + \sqrt{256}) (\sqrt[4]{255} + \sqrt[4]{256})}$ $= . . .$

Question Number 83910 Answers: 2 Comments: 1

find all 6 digit numbers which are not only palindrome but also divisible by 495.

$find all 6 digit numbers which are not$ $only palindrome but also divisible by 495 .$

Question Number 83874 Answers: 1 Comments: 1

Question Number 83871 Answers: 0 Comments: 4

If equation { (((√(x^2 +y^2 ))+(√((x−4)^2 +y^2 ))+(√(x^2 +(y−3)^2 ))+(√((x−4)^2 +(y−3)^2 ))=10)),((x+2y= 5z)) :} has solution is (a,b,c). find a+2b+3c

$If equation$ ${\begin{cases} \sqrt{x^{2} + y^{2}} + \sqrt{{(x - 4)}^{2} + y^{2}} + \sqrt{x^{2} + {(y - 3)}^{2}} + \sqrt{{(x - 4)}^{2} + {(y - 3)}^{2}} = 10 \\ x + 2 y = 5 z \end{cases}$ $has solution is (a, b, c) .$ $find a + 2 b + 3 c$