3^((x − 3)(x − y − 2)) = 1 5^((x^2 − 2xy + y^2 + x − y − 3/2)) = (√5) Find the value of x and y


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 13002 by Joel577 last updated on 10/May/17

$3^{(x - 3) (x - y - 2)} = 1$ $5^{(x^{2} - 2 x y + y^{2} + x - y - 3 / 2)} = \sqrt{5}$ $Find the value of x and y$
	Answered by 433 last updated on 10/May/17
	$3^((x−3)(x−y−2)) =3^0 (x−3)(x−y−2)=0 x=3 or x−y=2 if x=3 5^((9−6y+y^2 +3−y−(3/2))) =5^(1/2) 9−6y+y^2 +3−y−(3/2)=(1/2) y^2 −7y+10=0 y=5 or y=2 if x−y=2 5^(((x−y)^2 +(x−y)−(3/2))) =5^(1/2) 5^((4+2−(3/2))) =5^(1/2) 5^(3/2) =5^(1/2) (x,y)∈{(3,5),(3,2)}$
	$3^{(x - 3) (x - y - 2)} = 3^{0}$ $(x - 3) (x - y - 2) = 0$ $x = 3 o r x - y = 2$ $i f x = 3$ $5^{(9 - 6 y + y^{2} + 3 - y - \frac{3}{2})} = 5^{\frac{1}{2}}$ $9 - 6 y + y^{2} + 3 - y - \frac{3}{2} = \frac{1}{2}$ $y^{2} - 7 y + 10 = 0$ $y = 5 o r y = 2$ $i f x - y = 2$ $5^{({(x - y)}^{2} + (x - y) - \frac{3}{2})} = 5^{\frac{1}{2}}$ $5^{(4 + 2 - \frac{3}{2})} = 5^{\frac{1}{2}}$ $5^{\frac{3}{2}} = 5^{\frac{1}{2}}$ $(x, y) \in {(3, 5), (3, 2)}$
	Commented by Joel577 last updated on 11/May/17

	$t h a n k y o u v e r y m u c h$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum