how to find value √x+1/√x x=7+√40
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x = 7 + √40
x = 5 + 2 + 2√10
x =√5² + √2² + 2√5.√2
x = ( √5 + √2)²
take square root both sides
√x = ( √5 + √2)
hence, √x = ( √5 + √2)
so, 1/√x = 1/( √5 + √2) = ( √5 - √2)/3
now,
√x + 1/√x = ( √5 + √2) + ( √5 - √2)/3
= ( 3√5 + 3√2 +√5 -√2)/3
= ( 4√5 + 2√2)/3
x = 5 + 2 + 2√10
x =√5² + √2² + 2√5.√2
x = ( √5 + √2)²
take square root both sides
√x = ( √5 + √2)
hence, √x = ( √5 + √2)
so, 1/√x = 1/( √5 + √2) = ( √5 - √2)/3
now,
√x + 1/√x = ( √5 + √2) + ( √5 - √2)/3
= ( 3√5 + 3√2 +√5 -√2)/3
= ( 4√5 + 2√2)/3
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