Question

If $(15,a,b)$ form a pythagorean triplet, then find $(a,b)?$[4 marks]

Answer 1

For an integer m > 1 the numbers $m^2-1,2m$ and $m^2+1$ form a Pythagorean triplet.
[0.5 marks]

$\therefore$ $(m^2-1,2m$, $m^2+1)=$$(15,a,b)$
[0.5 marks]

$\Rightarrow m^2-1=15$

$\Rightarrow m^2=16=4^2$

$\Rightarrow m=4$
[1 mark]

$\therefore$$2m=2\times 4=8$
[0.5 marks]

And, $m^2+1=4^2+1=16+1=17$
[1 mark]

Hence, $(15,a,b)$ form a pythagorean triplet
So, $a=8$ and $b=17.$
$\therefore$ $(a,b)=$ $(8,17)$
[0.5 marks]