Relationship between two questions,tips(substitute)

Algebra Level 3

x 2 − y 2 = 29 , z 2 − x 2 = 31 x^2-y^2=29, z^2-x^2=31 , find the sum of z + x + y z+x+y where x , y , z ∈ N x,y,z\in N


The answer is 45.

Frankie Fook by Frankie Fook , 24, Malaysia

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Frankie Fook
Feb 27, 2015

x^2-y^2=29,29/2=14.5. It means that it may be 14<14.5<15, It means that value of x and y possibly be 14 or 15 since x^2-y^2=value of x is greater than y mean x=15 and y=14,equal to 15^2-14^2=29.z^2-15^2(value of x substitute from the first equation)=31, 31/2=15.5, it means that the possible value may be 16 or 15, since x=15 so z obviously equals to 16=16^2-15^2=31, x(15)+z(16)+y(14)=45

0 Helpful 0 Interesting 0 Brilliant 0 Confused

A better way to answer this is:

x^2 - y^2=29. ==> (x+y)(x-y) = 29. 29 is a prime number. Hence, x+y = 29...(A) and x-y = 1...(B). Solving A & B simultaneously x = 15, y=14 Now, x^2 = 225 Substitute that in z^2 - x^2 = 31 ==> z=16 Hence, z+x+y = 16+15+14 = 45

Sahil Shah - 6 years ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...