Question

Q1 : An Expression is given : 2 (√k - 1 ) + √8 if on adding -8√2 to the expression results in a rational numbers what is the value of k? ​

Answer 1

I can't answer see profile

Answer 2

Answer:

This is is not an equation to an expression which represents a positive real number which is either rational or not. According to Wolfram Alpha it equals 42–√42 and thus is not rational. From the preview for their reasoning I got this:

12±82–√=12±82=

4±8⋅2–√+8=4±8⋅2+8=

22±2⋅2⋅22–√+(22–√)2=22±2⋅2⋅22+(22)2=

(2±22–√)2(2±22)2

however because 2<22–√2<22

we need to make sure that the expression under the root isn’t negative and thus:

12−82–√−−−−−−−−√=22–√−212−82=22−2

while

12+82–√−−−−−−−−√=2+22–√12+82=2+22

and so

12−82–√−−−−−−−−√+12−82–√−−−−−−−−√12−82+12−82

becomes

2+22–√+22–√−22+22+22−2

which simplifies to

42–√42