Question #13424
1 Answer
Jan 8, 2018
We have:
Explanation:
Since
#x^2 + (3x- 5)^2 = 16#
#x^2 + 9x^2 -30x + 25 = 16#
#10x^2 - 30x + 9 = 0#
If we use the discriminant,
#30^2 - 4 * 10 * 9 = 540#
There will be two solutions, but since
#x= (-(-30) +- sqrt((-30)^2 - 4 * 10 * 9))/(2 * 10)#
#x= (30 +- sqrt(540))/20#
#x = (30 +- 6sqrt(15))/20#
#x = (15 +- 3sqrt(15))/10#
So the value of
#y = 3x -5#
#y = 3((15 +- 3sqrt(15))/10) - 5#
#y = (45 +- 9sqrt(15))/10 - 50/10#
#y = (-5 +- 9sqrt(15))/10#
We can confirm graphically:
Hopefully this helps!