3+2√2² +1÷3+2√2² what is the Answer of this question....
Answers
Step-by-step explanation:
Solution: Given,
=> 3•(2²ˣ⁻ʸ)/3 + 7•2/3 - 6 = 0
=> 3•(2²ˣ⁻ʸ)/3 = 6 - 14/3
=> 3•( 2²ˣ⁻ʸ )/3 = 4/3
• Taking log both side having base 10 , we have
=> log (3•( 2²ˣ⁻ʸ )/3) = log4/3
=> log2²ˣ⁻ʸ = log4/3
=> ( 2x -y )log2 = log4/3 [• logaⁿ = nloga ]
=> 2( 2x - y ) = 4/3 [• loga = logb , a=b ]
=> 2x - y = 2/3
=> 3( 2x - y ) = 2
=> 6x - 3y= 2
=> y = ( 6x - 2 )/3 - equation→(1)
And, log( 3x - y ) + log ( y + x) = 4log2
=> log(3x - y)( y + x ) = log2⁴ [• loga + logb = logab and nloga = logaⁿ ]
=> ( 3x - y )( x + y ) = 2⁴ [• log a = logb , a = b ]
=> 3x² - xy + 3xy - y² = 16
=>3x² + 2xy - y² = 16
=> 3x² + 2x•( 6x - 2 )/3 - ( 6x - 2 )²/3² = 16 [• y value from equation (1) ]
=> 3x² + ( 12x² - 4x )/3 - (36x² + 4 - 24x )/9 = 16
=> [ 27x² + 3(12x² - 4x ) - ( 36x² + 4 - 24x )] /9 = 16
=> 27x² + 36x²- 12x - 36x²- 4 + 24x =144
=> 27x² + 12x = 148
•This is quadratic equation ,
so, determinant of the equation is given by
=> D = b²- 4ac
=> D = 12² - 4x27 (-148)
=> D = 144 + 15984
=> D = 16128
And, √d = 48√7
• so, solution of quadratic equation is given as
=> x = ( b ± √D )/2a
=> x = ( 12 ± 48√7 ) / 2 x 27
=> x = 12 ( 1 ± 4√7 )/ 2 x 27
=> x = 2 ( 1 ± 4√7 ) / 9
=> x = ( 2 ± 8√7 ) / 9
• But argument of log cannot be negative
so, X = ( 2 + 8√7 ) / 9 -(2)
From equation (1) ,we have
=> y = ( 6x - 2 )/3
=> y=[ 6 ( 2 + 8√7 )/9 -2 ]/3 [• from equation (2), x = ( 2 + 8√7 )/9 ]
=> y = [ 2 (2 + 8√7 ) - 6 ]/9
=> y = ( 4 + 16√7 - 6 )/9
=> y = ( 16√7 - 2 )/9
•Therefore solution of systems of equations are
X = ( 2 + 8√7 )/9 , Y= ( 16√7 - 2 )/9