Question #52ae1

1 Answer
Dec 31, 2014

#k=+-5/2#

You have #4x^2-8kx+9=0#
and you know that the two solutions, #x_2 and x_1#, are related as:
#x_2-x_1=4#

You solve your equation with #k# in place:
#x_(1,2)=(8k+-sqrt(64k^2-4(4*9)))/8#
Giving:
#x_(1,2)=(8k+-sqrt(64k^2-144))/8#
These are two solutions: one with the + sign and the other with the - sign. Substituting in: #x_2-x_1=4# you get
#(8k+sqrt(64k^2-144))/8-(8k-sqrt(64k^2-144))/8=4#
rearranging and taking as common denominator #8# you'll get:
#2*(sqrt(64k^2-144))=32#
#(sqrt(64k^2-144))=16#
#64k^2-144=256#
#k=sqrt(400/64)=+-5/2#