Question

26. If x=√5-√3/√5+√3
then find the value of x2 - 8x + 1.​

Answer 1

Answer:

x2-8x+1=0

Step-by-step explanation:

x=(√5-√3)/(√5+√3)

Rationalize the denominator

x= ((√5-√3)(√5-√3))/((√5+√3)(√5-√3))

x=((√5-√3)^2)/((√5+√3)(√5-√3))

For numerator,

${(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab$

For denominator,

$(a + b)(a - b) = {a}^{2} - {b}^{2}$

x= (5+3-2√15)/(5-3)

x=(8-2√15)/2

x=2(4-√15)/2

x=4-√15

x2-8x+1

=(4-√15)^2-8(4-√15)+1

=16+15-8√15-32+8√15+1

=16+16-32

=0