Question

if a=3-√5 find the value of a sq.+ 1/ a sq.

Answer 1

ʜᴇʟʟᴏ ᴍᴀᴛᴇ

ᴀ = 3 - √5
ᴀ² = ( 3 - √5 )²
= 9 + 5 - 2*3*√5
= 14 - 6√5

1/ᴀ = 1/( 3 - √5 ) × ( 3 + √5 )/( 3 + √5 )
= ( 3 + √5 )/( 9 - 5 ) = ( 3 + √5 ) / 4

1/ᴀ² = [ ( 3 + √5 )/4 ]² = ( 14 + 6√5 )/16
ᴏʀ ( 7 + 3√5 )/8

ᴀ² + 1/ᴀ²

( 14 - 6√5 ) + ( 7 + 3√5 )/8

( 112 - 48√5 + 7 + 3√5 )/8

= ( 119 - 45√5 )/8

ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs