New concepts
x + x 1 = x 2 1 + x 2 1 1
The equation above has repeated real roots, and two conjugate complex roots of the form 2 − a ± i b , where a and b are positive integers. What is the value of a + b ?
The answer is 4.
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1 solution
Good question. But ask the moderators for latex expression like
x + x 1 = x + x 1
NOw say that if two equal rootsis represented by a
And two imaginary roots are given by x = 2 − a + i b `
And a and b are coprime +ve integers find a + b .
O.K. thanks for all staff members especially ; Mr. Calvin Lin. Mr. Md Zuhair. Mr. Pi Han Goh.
X+1/x = √x+1/√x. squaring both sides we get : (X+1/x)² = X+1/x+2.
Let X+1/x = m , m² = m+2 , m² -m-2=0 , m = 2,-1. For , m =2 = X+1/x , we get the two equal roots =1. For , m =-1 = X+1/x , we get the two conjugate complex roots = (-1±√3i)/2. Therefore , a+b=1+3=4.