Question

If x=7+√40, find the value of√x + 1 ÷ √x

Answer 1

x=7+√40
=7+2√10
=5+2+2√10
=(√5)²+2.√5.√2+(√2)²
=(√5+√2)²
∴√x=√5+√2 (neglecting the negative sign)
1/√x=1/(√5+√2)
=(√5-√2)/(√5+√2)(√5-√2)
=(√5-√2)/(5-2)
=(√5-√2)/3
√x+1/√x
=(√5+√2)+(√5-√2)/3
=(3√5+3√2+√5-√2)/3
=(4√5+2√2)/3
=2(2√5+√2)/3

Answer 2

x=7+√40

=7+2√10

=5+2+2√10

=(√5)²+2.√5.√2+(√2)²

=(√5+√2)²

∴√x=√5+√2 (neglecting the negative sign)

1/√x=1/(√5+√2)

=(√5-√2)/(√5+√2)(√5-√2)

=(√5-√2)/(5-2)

=(√5-√2)/3

√x+1/√x

=(√5+√2)+(√5-√2)/3

=(3√5+3√2+√5-√2)/3

=(4√5+2√2)/3

=2(2√5+√2)/3