If α and β are the root of the equation 2X²-7X-3=0 Find α/β+1 + β/α+1
Working answer please
It is α/β+1 + β/α+1
That is how the question is
x = [ 7 +/- sqrt (49 + 24) ] / 4
α = (7+sqrt 73)/4
β = (7-sqrt 73)/4
now I do not care to go on because I am not sure if you mean what you typed
(α/β)+1
or
α/ (β+1)
But it is not typed on one line in your book.
What is the numerator and what is the denominator?
You need more parentheses when typing online.
a
---- + 1
b
or
a
------
b+1
α/β + 1 + β/α + 1
Sorry its error in tying
α
---- + 1
β
α/β + 1 + β/α + 1 = α/β + β/α + 2
I still think you may have it wrong
are you sure you do not mean:
α/(β + 1)
+
β/(α + 1 )
Okay .. Please you can still help out with
α/(β + 1)
+
β/(α + 1 )
β+1 = (7-sqrt 73)/4 + 4/4 = (11-sqrt 73)/4
α+1 = (7 +sqrt 73)/4 + 4/4 = (11+sqrt 73)/4
α/(β + 1) = (7+sqrt 73)/(11-sqrt73)
β/(α + 1 ) = (7-sqrt 73)/(11+sqrt 73)
α/(β + 1) = (7+sqrt 73)/(11-sqrt73) * (11+sqrt73)/(11+sqrt73)
β/(α + 1 ) = (7-sqrt 73)/(11+sqrt 73) * (11-sqrt 73)/(11-sqrt 73)
α/(β + 1) = (7+sqrt 73)* (11+sqrt73)/(121-73)
β/(α + 1 ) = (7-sqrt 73) * (11-sqrt 73)/(121- 73)
(77 +18 sqrt 73 +73)/48
(77 - 18 sqrt 73 +73/48
-------------------------------- add
(154 + 146) /48
= 150/48