Question

if x=√7+4√3/7-4√3 then find x^2(x+14)^2

Answer 1

Hi ,

1 ) √7 + 4√3

= √7 + 2√6

= √ (√6 )² + 1² + 2 × √6 × √1

= √ ( √6 + 1 )²

= √6 + 1 ---( 1 )

2 ) similarly ,

√7 - 4√3 = √6 - 1----( 2 )

It is given that ,


x = √[( 7 + 4√3 )/( 7 -4√3 ) ]

x =√[ ( √6 + 1 )/ ( √6 - 1 )]

x =√ [ (√6+1 ) ( √6 + 1 )]/[ (√6 - 1 )( √6 + 1 ) ]

x = √ [ (√6 + 1 )²/5 ]

x = ( √6 + 1 )/√5 ---( 3 )

do the square of equation ( 3 ) , we get

x² = ( √6 + 1 )² /5

x² = ( 6 + 1 + 2√6 ) /5

x² = (7 + 2√6 )/5 ---( 4 )

x²( x + 14 )² = x²(x² + 28x + 196)

= [(7+2√6)/5][(7+2√6 )/5 +28[ (√6 +1)/√5+196]

I hope this helps you.

: )

Answer 2

Answer:

[a(a-14)]^2 = 1

Step-by-step explanation:

Formula used

a^2 - b^2 = (a+b) (a-b)