questions 8) help me guys
Answers
Question 8
(a) x + y = (√5 + √2 ) / ( √5 - √ 2 ) + (√5 - √2 ) / ( √5 + √2 )
==>( (√5 + √2 )² + (√5 - √2 )² ) / (√5² - √2² )
==> ( 5 + 2 + 2√10 + 5 + 2 - 2√10 ) / ( 5 - 2 )
==> 14/3
( x + y )² = 196/9
3 ( x + y )² = 196/3
==> 3 x² + 3 y² + 6 xy = 196/3
Subtract 2 xy both sides
==> 3 x² + 3 y² + 4 xy = 196/3 - 3 xy
==> 196/3 - 3 ( √5 + √2 )/ (√5 - √2 ) (√5 - √2 ) / ( √5 + √2 )
==> 196/3 - 3 ( 5 - 2 ) / ( 5 - 2 )
==> 196/3 - 3×1
==> 196/3 - 3
==> ( 196 - 27 ) / 3
==> 169/3
The value is 169/3
(b)
a⁴ + 4
==> (a²)² + 2²
==> ( a²)² + 2² + 4 a² - 4 a²
==> ( a² + 2 )² - 4 a²
==> ( a² + 2 )² - ( 2 a )²
==> ( a² + 2 + 2 a )( a² + 2 - 2 a )
Answer : (a² + 2 + 2a )( a² + 2 - 2a)
( x² + 1/x² ) + 2 ( x - 1/x ) - 5
==> ( x⁴ + 1 ) /x² + 2 ( x² - 1) / x - 5
==> ( x⁴ + 1 + 2 x ( x² - 1 ) - 5 x² ) / x²
==> ( x⁴ + 1 - 2 x² + 2 x ( x² - 1 ) - 3 x² ) / x²
==> ( ( x² - 1 )² + 2 x ( x² - 1 ) - 3 x² ) /x²
==> ( ( x² - 1 )( x² - 1 + 2 x ) - 3 x² ) / x²
==> ( ( x + 1 )( x - 1 )( (x + 1 )( x - 1 ) + 2 x ) - 3 x² ) / x²
(c) There are two polygons of sides n - 1 and n + 2
We know that n sided regular polygon has 360 / n - 1 exterior angle
According to the question :
360 / ( n - 1 ) - 360 / ( n + 2 ) = 6
==> ( 360 ( n + 2 ) - 360 ( n - 1 ) ) = 6 ( n - 1 )( n + 2 )
==> 360 n + 720 - 360 n + 360 = 6 ( n² - n + 2 n - 2 )
==> 1080 = 6 ( n² - 3 n - 2 )
==> n² + n - 2 = 180
==> n² - n - 182 = 0
==> n² - 14 n + 13 n - 182 = 0
==> n ( n - 14 ) + 13 ( n - 14 ) = 0
==> ( n - 14 )( n + 13 ) = 0
Either n = 14
or , n = -13
number of sides = 14 as it cant be negative.
The number of sides is 14.
I cannot help you more :-(
Hope I helped you
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