Can you draw an equilateral right triangle? Explain using precise mathematical language.

No.

Step-by-step explanation:

An equilateral triangle is made when all three sides of the triangle are congruent, which means that the angles will also be congruent. A right triangle is defined by its 90° angle. The total angle measures of a triangle add up to 180°. This means that the other two angles have to add up 90° because one measure is already half of 180. Since the measures have to add up to 90, they won't each be equal to 90. This means that the triangle won't be equilateral. (or, you can't have three 90° angles in a triangle because that would pass the 180° measure)

Also, the use of the Pythagorean theorem shows that the sum of the legs squared is equal to the hypotenuse. Thus, the hypotenuse in a right triangle will always be the longest side, which means that it can't be an equilateral triangle.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this