How do you find the solution to the quadratic equation #2x^(2/3) + 5^(1/3) = 12#?

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Answer 1 · 2015-05-09T17:57:51

In this way:

let #x^(1/3)=t# so #x^(2/3)=t^2#.

#2t^2+5t-12=0#

#Delta=b^2-4ac=25+4*2*12=121#

#t=(-b+-sqrtDelta)/(2a)=(-5+-11)/4rArr#

#t_1=(-5-11)/4=(-16)/4=-4#

#t_2=(-5+11)/4=6/4=3/2#.

And now:

#x^(1/3)=-4rArr(x^(1/3))^3=(-4)^3rArrx=-64#

#x^(1/3)=3/2rArr(x^(1/3))^3=(3/2)^3rArrx=27/8#.