Question #21708

The heights (in metres) of two men satisfy the quadratic equation 40x^2 - 138x + 119 =0 Without solving the equation, find the average height of these two men.

Expert's answer

Let x1, x2 - roots of the equation (and it is heights of two men);we can use Vieta's theorem to find x1+x2.

To do this we can rewrite equation as

x^2-(138/40)*x+119/40=0

Now, from Vieta's theorem x1+x2=-(-138/40)=138/40 averageheight=(x1+x2)/2=138/80=69/40=1.725 metres

To do this we can rewrite equation as

x^2-(138/40)*x+119/40=0

Now, from Vieta's theorem x1+x2=-(-138/40)=138/40 averageheight=(x1+x2)/2=138/80=69/40=1.725 metres

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