Olympiad Mathematics | The first solution doesn't satisfy | Why?

This is beautifully solved for you #olympiad #exponential #equation #maths #mathstricks #education #exponentialequation #algebra

[@goabaonesekalaba2830]

❤❤

[@PhilCoolMath]

Thanks so much ❤️

[@davidbrisbane7206]

Let y = √x and then solve the quadratic in y and then solve for x.

[@juergenilse3259]

You do not need tosquare both sides, if ou dothe foowing substitution: Let t=sqrt(x), tthen we get: t+t^2=3/4 t^2+t-3/4=0 t=-1/2+-sqrt((1/2)^2-(-3/4)) t=-1/2+-sqrt(1/4+3/4) t=-1/2+-sqrt(1) t=-1/2+1=1/2 or t=-1/2-1=-3/2 Recall t=sqrt(x), and thinof definition of square root of x as the non negative soution of t^2=x: We reject t=-3/2, since it is ower than 0. So t=1/2 and x=t^2=(1/2)^2=1/4 With squaring the equation, you have the risk to get additiona (errornous) soutions.

[@RyanLewis-Johnson-wq6xs]

Sqrt[x]+x=3/4 x=0.25=1/4

[@tinkerman9525]

Something that basic takes a long time😂😂😂😂😂😂 73's