V5+12 If x= 5-12 y = V5 - 2 5+ 2 then find the value of 3x²+4xy+3y? Pls answer step by step
Answers
Answer:
Step-by-step explanation:
Hey there !!
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Given, x = ( √5 – 2 ) / ( √5 + 2 ) and y = ( √5 + 2 ) / ( √5 – 2 )
x = ( √5 – 2 ) / ( √5 + 2 )
= ( √5 – 2 ) / ( √5 + 2 ) × ( √5 – 2 ) / ( √5 – 2 )
= ( √5 – 2 )² / [ (√5)² – (2)² ]
= ( 9– 4√5 ) / ( 5 – 4 )
= 9 – 4 √5
y = ( √5 + 2 ) / ( √5 – 2 )
= ( √5 + 2 ) / ( √5 – 2 ) × ( √5 + 2 ) / ( √5 + 2 )
= ( √5 + 2 )² / [ (√5)² – (2)² ]
= ( 9 + 4√5 ) / ( 5 – 4 )
= 9 + 4√5
Now, x² + xy + y²
= ( 9 – 4√5 )² + ( 9 – 4√5)( 9 + 4√5 ) + ( 9 + 4√5 )²
= ( 81 – 72√5 + 80 ) + [ 9( 9 + 4√5 ) –4√5( 9 + 4√5 ) ] + ( 81 + 72√5 + 80 )
= ( 161 – 72√5 ) + ( 81 + 13√5 – 13√5 – 80 ) + ( 161 + 72√5 )
= 161 – 72√5 + 1 + 161 + 72√5
= 161 + 1 + 161
= 323
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Hope it's satisfactory. (^-^)