Latest Elitmus Aptitude Question SOLUTION: Find the sum of roots of the equation root(x+7)=xroot(x+7)

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Find the sum of roots of the equation
root(x+7)=xroot(x+7)

Asked In Elitmus Vaibhav Sharma (9 years ago)

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burri jagadish  (9 years ago)

root(x+7)=x*root(x+7)

by squaring on both sides....

(x+7)=(x^2) * (x+7)
by cancelling both sides
1= x^2
the roots are x= 1 and -1
the sum of roots = 1+(-1)=0

Is this solution Helpfull? Yes (14) | No (8)  

Nitish saxena  (9 years ago)

squaring both sides
x+7=x^2(x+7)
x+7=x^3+7x^2
x^3+7x^2-x-7=0
by hit and trial
x=1
it will satisfy
now divide the equation with x-1
x^3+7x^2-x-7/x-1 =x^2+8x+7
solving the quadratic eqation will give roots -7,-1
now sum will be 1+(-7)+(-1)=-7
Answer=-7

Is this solution Helpfull? Yes (12) | No (8)  

sahanashree H N  (9 years ago)

squaring on both the sides
(x+7)=x^2 (x+7)
(x+7) - x^2(x+7) = 0
(x+7) [1 - x^2)=0
x = -7 , x = 1
sum = -7+1 = -6

Is this solution Helpfull? Yes (8) | No (11)  

Ashok kumar  (9 years ago)

squaring on both sides
x+7=x^2(x+7)
x^2(x+7)-(x+7)=0
(x^2-1)(x+7)=0
the roots are x=1 & -1 , x=-7
sum of the roots are 1+(-1)+(-7)= -7

Is this solution Helpfull? Yes (5) | No (5)  

md shahjad khan  (9 years ago)

rootI(x+7)=xroot(x+7)
squaring we get
x+7=x^2(x+7)
(x+7)(x^2-1)=0
x+7=0 or x^2-1=0
x=-7 or x^2=1
x=-7 or x=1 or x=-1
now put the all values in given equation root(x+7)=xroot(x+7)
we get x=-1 does not satisfy the equation
so value will be x=-7 and 1
hence, sum of roots=1-7= -6

Is this solution Helpfull? Yes (4) | No (8)  

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