Question

if X=1/7+4√3 and y= 1/ 7-4✓3​

Answer 1

Answer:

If x = √ (7+4√3) /√ (7-4√3) , then what does x² (x-14) ² =?

Let me make Sanjay’s answer more clear by showing the steps that he skipped:

Solving for x2(x−14)2 for x=7+43√√7−43√√

Like he said, we should rationalize the denominator using the identity (a+b)(a−b)=a2−b2 This identity is called the difference of squares identity

and the goal of rationalization is to multiply the top and bottom by a number such that it will get rid of the radicals in the denominator - this number is called the conjugate

for example the conjugate of a−−√+b√ is a−−√−b√ as multiplying the two together will get rid of the

If x=7+4√3, then what will be the value of √x+1/√x?

If x=√7+4√3, what is the value of x+1/x=?

If a=√ (7+4√3), what will be the value of a+1÷a?

If x=√7+4√3, what is the value of x+1÷x?

If x=√7+4√3, then what us the value of [x+1\x]?

x^2 = (7 + 4 sqrt(3)/(7 - 4 sqrt(3)) * (7 + 4 sqrt(3))/(7 + 4 sqrt(3))

x^2 = (7 + 4 sqrt(3))^2/((7 - 4 sqrt (3))(7 + 4 sqrt(3))

x^2 = (7 + 4 sqrt(3))^2/(49 - 16 * 3)

x^2 = (7 + 4 sqrt(3))^2

Taking the square root of both sides,

x = 7 + 4 sqrt (3) = 4 sqrt (3) + 7, because x > 0

x - 14 = 7 + 4 sqrt(3) - 14 = 4 sqrt(3) - 7

x^2 (x - 14)^2

= (x * (x - 14))^2

= ((4 sqrt (3)+ 7)(4 sqrt(3) - 7))^2

= ((4 sqrt (3))^2 - 7^2)^2

= (16 *3 - 49)^2

= (48 - 49)^2

= 1