Question 46

Let A = {(a, b, c)/ $$c^2$$ = $$a^2 + b^2$$ }. If (3, 5, x), (y, 3, 7), (1, z, 5) are three elements of the set 'A' and the LCM of $$x^2, y^2, z^2$$ is $$p_1^{\alpha_1} p_2^{\alpha_2} p_3^{\alpha_3} p_4^{\alpha_4}$$ where $$p_1, p_2, p_3, p_4$$ are primes, then $$\frac{p_1 + p_2 + p_3 + p_4}{\alpha_1 + \alpha_2 + \alpha_3 + \alpha_4}$$ =

Solution

It is given that ,$$c^2=a^2+b^2$$.

Now,if you compare set(a,b,c) with set(3,5,X) then we can say that a=3,b=5 & c=x.

So,$$x^2=3^2+5^2$$

or,x=√(9+25)=√34.

Similarly,

$$y=√(49-9)=√40$$ and

$$z=√(25-1)=√24$$

so,$$LCM(x^2,y^2,z^2)=LCM(34,40,24)$$

$$=2^3×17×5×3.$$

so,$$p1+P2+P3+p4=2+17+5+3=27.$$

and $$a1+a2+a3+a4=3+1+1+1=6$$

so,ratio would be$$=27/6=9/2.$$

A is correct choice.

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