Question

If x = 7- 4√3 find the value of x²- 1 ÷ x²​

Answer 1

Answer:

here is you answer mate

Step-by-step explanation:

x=7−43

∴x1=(7−43)1×7+437+43

=(49−48)7+43

=7+43

Now,

x+x1=(7−43)+(7+43)

=14

=>(x+x1)2=(14)2

Using (a+b)2=a2+b2+2ab we get,

=>x2+x21+2(x)(x

Answer 2

Answer: 194

Step-by-step explanation:

Given,

x = 7-4$\sqrt{3$

∴ $\frac{1}{x}$ = $\frac{1}{(7-4\sqrt{3} )}$×$7 +4\sqrt{3} \\7 +4\sqrt{3}$   = $7+ 4\sqrt{3}$

now,

x+$\frac{1}{x}$ = $(7 - 4\sqrt{3})$ + $(7+4\sqrt{3} )$ = 14

⇒ $(x+\frac{1}{x})^{2}$=$(14)^{2}$

⇒$x^{2} +\frac{1}{x^{2} }$= 196-2

so,

$x^{2} +\frac{1}{x^{2} }$= 194