repost question from mr jagoll { ((2+6y = (x/y)−(√(x−2y)))),(((√(x+(√(x−2y)))) = x+3y−2 )) :}


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 91786 by john santu last updated on 03/May/20

$r e p o s t q u e s t i o n f r o m$ $m r j a g o l l$ ${\begin{cases} 2 + 6 y = \frac{x}{y} - \sqrt{x - 2 y} \\ \sqrt{x + \sqrt{x - 2 y}} = x + 3 y - 2 \end{cases}$
Commented by john santu last updated on 03/May/20
$(1)6y = ((x−2y)/y) −(√(x−2y)) 6 = ((x−2y)/y^2 )−((√(x−2y))/y) set w = ((√(x−2y))/y) ⇒6=w^2 −w w^2 −w−6 = 0 (w−3)(w+2) = 0 ⇒(i) w=3 =((√(x−2y))/y) ,y>0 (√(x−2y)) = 3y ; x = 9y^2 +2y ⇒(√(x+3y)) = x+3y−2 (√(9y^2 +5y)) = 9y^2 +5y−2 set (√(9y^2 +5y)) = p, p>0 p^2 −p−2=0 ⇒p=2 9y^2 +5y−4=0 y = ((−5 ± 13)/(18)) { ((y_1 =−1; not solution)),((y_2 = (4/9);x_2 = ((24)/9))) :} ⇒(ii) w=−2 =((√(x−2y))/y) , y<0 −2y = (√(x−2y)) ⇒x=4y^2 +2y ⇒(√(x−2y)) = x+3y−2 −2y = x+3y−2 ; x+5y−2=0 4y^2 +7y−2=0 (4y−1)(y+2)=0 { ((y_3 = (1/4); no solution)),((y_4 =−2 ; x_4 =12 )) :} finally solution is (((24)/9), (4/9)) ∧ (12,−2)$
$(1) 6 y = \frac{x - 2 y}{y} - \sqrt{x - 2 y}$ $6 = \frac{x - 2 y}{y^{2}} - \frac{\sqrt{x - 2 y}}{y}$ $s e t w = \frac{\sqrt{x - 2 y}}{y} \Rightarrow 6 = w^{2} - w$ $w^{2} - w - 6 = 0$ $(w - 3) (w + 2) = 0$ $\Rightarrow (i) w = 3 = \frac{\sqrt{x - 2 y}}{y}, y > 0$ $\sqrt{x - 2 y} = 3 y; x = 9 y^{2} + 2 y$ $\Rightarrow \sqrt{x + 3 y} = x + 3 y - 2$ $\sqrt{9 y^{2} + 5 y} = 9 y^{2} + 5 y - 2$ $s e t \sqrt{9 y^{2} + 5 y} = p, p > 0$ $p^{2} - p - 2 = 0 \Rightarrow p = 2$ $9 y^{2} + 5 y - 4 = 0$ $y = \frac{- 5 \pm 13}{18} {\begin{cases} y_{1} = - 1; n o t s o l u t i o n \\ y_{2} = \frac{4}{9}; x_{2} = \frac{24}{9} \end{cases}$ $\Rightarrow (i i) w = - 2 = \frac{\sqrt{x - 2 y}}{y}, y < 0$ $- 2 y = \sqrt{x - 2 y} \Rightarrow x = 4 y^{2} + 2 y$ $\Rightarrow \sqrt{x - 2 y} = x + 3 y - 2$ $- 2 y = x + 3 y - 2; x + 5 y - 2 = 0$ $4 y^{2} + 7 y - 2 = 0$ $(4 y - 1) (y + 2) = 0$ ${\begin{cases} y_{3} = \frac{1}{4}; n o s o l u t i o n \\ y_{4} = - 2; x_{4} = 12 \end{cases}$ $f i n a l l y s o l u t i o n$ $i s (\frac{24}{9}, \frac{4}{9}) \land (12, - 2)$
Commented by jagoll last updated on 03/May/20

$w a w . . . g r e a t m r j o h n . t a n k a l o t$
Commented by niroj last updated on 03/May/20
✔��
Commented by john santu last updated on 03/May/20

$h o w t o m a k e t h i s s y m b o l$ $m r N i r o ?$
Commented by niroj last updated on 03/May/20

$go to more & tap last option add plaintext comment$ $dear mr . john santu$
Commented by jagoll last updated on 03/May/20
good ^o^
Commented by john santu last updated on 03/May/20
��
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum