if x = 3+2 root 2 find find root x+1/root x
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x=3+2√2
or, x=2+1+2√2
or, x=(√2)²+2×√2×1+(1)²
or, x=(√2+1)²
∴, √x=√2+1 (neglecting the negative sign)
∴1/√x=1/(√2+1)
=(√2-1)/(√2+1)(√2-1)
=(√2-1)/{(√2)²-(1)²}
=(√2-1)/(2-1)
=√2-1
∴, √x+1/√x
=√2+1+√2-1
=2√2
or, x=2+1+2√2
or, x=(√2)²+2×√2×1+(1)²
or, x=(√2+1)²
∴, √x=√2+1 (neglecting the negative sign)
∴1/√x=1/(√2+1)
=(√2-1)/(√2+1)(√2-1)
=(√2-1)/{(√2)²-(1)²}
=(√2-1)/(2-1)
=√2-1
∴, √x+1/√x
=√2+1+√2-1
=2√2
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