Fives everywhere

Algebra Level 2

The equation $(5 \times 5 \times 5 \times x) = 2(5 + 5 + 5 + x)^{2}$ has two solutions. If we call them a and b, find $a \times b$ .

2 solutions

Nelson Mandela
Jul 17, 2015

by simplifying the given expression we get 2x^2-65x+450=0.

product of roots is c/a in the equation ax^2+bx+c. so directly answer is 450/2 = 225.

Denton Young
Jul 17, 2015

The equation can be written as $125x$ = $2(15 + x)^{2}$

simplifying, $2x^{2} - 65x + 450 = 0$

Factoring, $(x-10)(2x-45) = 0$

x = 10 or x = 22.5

10 * 22.5 = 225

actually there is no need for knowing the roots. directly product of roots is c/a in the equation ax^2+bx+c. so directly answer is 450/2 = 225.

Nelson Mandela - 5 years, 11 months ago

In this case, true. But suppose I had asked for a + b instead? Always best to know the roots if you can.

Denton Young - 5 years, 11 months ago

and for a+b directly it is -b/a in ax^2+bx+c.

So, a+b is 65/2 = 32.5 directly. so this is just a simple question and it is being complicated by finding the roots.

Nelson Mandela - 5 years, 11 months ago