Born on the inflation and
scarity stricken 1960s and 70 this well paid adults
enjoy their new wealth , but conservation in
their spending and investing habits .They swing
among confidence and caution when it comes to money
Answers
Answer:
Explanation:
Too much cash in savings accounts is a well-kept secret of personal finance. Many of the self-employed, like doctors, entrepreneurs and lawyers, and well-paid salaried professionals do not make investment decisions, but allow money to lie in the bank, earning returns that do not even beat inflation. How is it that otherwise accomplished professionals do not follow the basic principles of wealth management?
Perhaps they suffer from the burden of choice. When there are too many choices, ..
Answer:
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Given :-
The quadratic equation (a-b)x²+(b-c)x+(c-a)=0 are equal real roots.
To prove :-
2a=b+c
Theory :-
For a Quadratic equation of the form
ax²+bx+c= 0 , the expression b²-4ac is called the discriminant.
Nature of roots:-
The roots of a quadratic equation can be of three types.
If D>0, the equation has two distinct real roots.
If D=0, the equation has two equal real roots.
If D<0, the equation has no real roots.
Solution :
We have , (a-b)x²+(b-c)x+(c-a)=0
On comparing with the standard form of Quadratic equation ax²+bx+c= 0.
Here ,
a= (a-b)
b= (b-c)
and c = (c-a)
When equation have equal ro ots then,
Discriminant = 0
\sf{\implies ({b-c}) ^{2} - 4(a-b)(c-a)=0 }⟹(b−c)
2
−4(a−b)(c−a)=0
\sf{\implies {b}^{2} + {c}^{2} - 2cb - 4ac + 4 {a}^{2} + 4bc - 4ab = 0 }⟹b
2
+c
2
−2cb−4ac+4a
2
+4bc−4ab=0
\sf{\implies {b}^{2} + {c}^{2} + 4 {a}^{2} + 4bc - 4ac - 4 ab = 0 }⟹b
2
+c
2
+4a
2
+4bc−4ac−4ab=0
\sf{\implies {b}^{2} + {c}^{2} +( {-2a})^{2}+2bc + 2c(-2a) + 2(-2a)b = 0}⟹b
2
+c
2
+(−2a)
2
+2bc+2c(−2a)+2(−2a)b=0
\sf{\implies {(b+c-2a)}^{2} = 0 }⟹(b+c−2a)
2
=0
\sf{\implies b + c -2a = 0 }⟹b+c−2a=0
Hence proved ✔
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