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After getting XY=9 & Y>X >0;Suppose X&Y=a√37±a; =>XY=(a√37+a)(a√37-a); => XY=a^2(37) -a^2; Recall XY=9; =>a^2(37-1)=9; ,=>a^2=9/36; a=±1/2;X&Y=(√37±1)(1/2); for Y>X =>X=(√37-1)(1/2)
(x^3+Sqrt[196])/(Sqrt[37])=5 x=0.5Sqrt[37]-0.5=(Sqrt[37]-1)/2 x=-0.25Sqrt[37]+0.25±(0.25Sqrt[111]-0.25Sqrt[3])i
X= (√ 37-1)/2
X=([-1+(37)^(1/2)]/2, [-1-(37)^(1/2)]/2.)
X is 3
This use of unnecessary algebra is not worth watching these videos. Just take the cube root of both sides after isolating x. That’s it. Then you can show using Descartes rule of sign that there’s only 1 sign change so at most 1 positive real root.
[(37)^(1/2)-1]/2
After getting XY=9 & Y>X >0;
Suppose X&Y=a√37±a; =>
XY=(a√37+a)(a√37-a); =>
XY=a^2(37) -a^2; Recall XY=9; =>
a^2(37-1)=9; ,=>
a^2=9/36; a=±1/2;
X&Y=(√37±1)(1/2); for Y>X =>X=(√37-1)(1/2)
(x^3+Sqrt[196])/(Sqrt[37])=5 x=0.5Sqrt[37]-0.5=(Sqrt[37]-1)/2 x=-0.25Sqrt[37]+0.25±(0.25Sqrt[111]-0.25Sqrt[3])i
X= (√ 37-1)/2
X=([-1+(37)^(1/2)]/2, [-1-(37)^(1/2)]/2.)
X is 3
This use of unnecessary algebra is not worth watching these videos. Just take the cube root of both sides after isolating x. That’s it. Then you can show using Descartes rule of sign that there’s only 1 sign change so at most 1 positive real root.
[(37)^(1/2)-1]/2