if a,b are real numbers, then
a²≤b² iff |a|≤|b|
Answers
Step-by-step explanation:
Discriminant of the equation in x will be found to be −4(b
2
−ac)
2
which is ≤0
But, for real x, it cannot be negative and so it must have b
2
−ac=0 showing that a,b,c are in G.P.
Under this condition, the equation has equal roots say x,x
Therefore, the sum of the roots is x+x=
a
2
+b
2
2b(a+c)
⟹x=
a
2
+ac
b(a+c)
(since, b
2
=ac)
⟹x=
a
b
=
b
c
is the common ratio.
Answer:
Solution
verified
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Discriminant of the equation in x will be found to be −4(b
2
−ac)
2
which is ≤0
But, for real x, it cannot be negative and so it must have b
2
−ac=0 showing that a,b,c are in G.P.
Under this condition, the equation has equal roots say x,x
Therefore, the sum of the roots is x+x=
a
2
+b
2
2b(a+c)
⟹x=
a
2
+ac
b(a+c)
(since, b
2
=ac)
⟹x=
a
b
=
b
c
is the common ratio.
Step-by-step explanation:
hope it will help you