Difference of Squares

Number Theory Level 1

If $a$ and $b$ are positive integers such that $a^2-b^2=7$ , then find $a-b$ .

3 solutions

Hjalmar Orellana Soto
Nov 1, 2015

$a^{2}-b^{2}=7$

$=>(a+b)(a-b)=7$

$a$ and $b$ are positive integers, so $a+b=7$ and $a-b=1$

(a+b)(a-b)=7a how is this possible?

Saiful Haque - 5 years, 7 months ago

a=4 e b=3 satisfaz o problema

Matheus Lima - 5 years, 7 months ago

Andrew Adair
Nov 4, 2015

Alt. Method? Sq. - Sq. is 7. Look for 2 Sq.s where difference between is 7 (16 & 9). 4 - 3 = 1.

Saiful Haque
Nov 1, 2015

a^2-b^2=7 or,(a+b)(a-b)=7*1 then,a+b=7 and a-b=1