Question

If(√14/√7-2)-(√14/√7+2)=a√7+b√2 find the values of a and b where a and b are rational numbers​

Answer 1

• a = 4/3 and b = 0

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Given expression:

`(√(14) )/(√(7)-2) -(√(14) )/(√(7)+2)`

Simplify it in steps:

Step 1

Bring both fractions into common denominator:

`(√(14) (√(7)+2))/((√(7)-2)(√(7)+2)) - (√(14) (√(7)-2))/((√(7)-2)(√(7)+2))`

Step 2

Simplify:

`(√(14) ((√(7)+2) - (√(7)-2)))/((√(7)-2)(√(7)+2)) =`

`(√(14) (√(7)+2 - √(7)+2))/((√(7)-2)(√(7)+2)) =`

`(4√(14) )/((√(7)-2)(√(7)+2)) =`

`(4√(14) )/((√(7))^2-2^2) =`

`(4√(14) )/(7-4) =`

`(4)/(3) √(14) }`

Step 3

Compare the result with given expression to get:

• a = 4/3 and b = 0