Question

Rationalize and solve for x in the following:


`a)(3)/(1-√(2) ) \\\\b)\sqrt[3]{4+x}=3\\\\c)\sqrt{3x^(2) }-√(12)=0\\\\d)√(18)-x√(2)=√(32)`

Answer 1

A) don't see an x B) x=23 C) x=2; D) x=-1

Explanation:

B) Cube both sides...
`(\sqrt[3]{4+x})^3=3^3`---> 4+x=27

C) add
`√(12)` to both sides...
`√(3x^2)=√(12)`... square both sides...
`(√(3x^2))^2=(√(12))^2`--> 3x^2=12... divide both sides by 3--> x^2=4---> x=2

D=
`√(18)-(x*√(2))=√(32)`... divide each side
`√(2)` --->
`(√(18)/√(2))- [(x*√(2))/√(2)]= √(32)/√(2)`--->
`√(9)-x= √(16)`... and because 9 and 16 are perfect squares our equation now reads---> 3-x=4---> -x=1---> x=-1