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Damm [24]
2 years ago
10

If a,b,c are all non-zero numbers and a+b+c=0, prove that

Mathematics
1 answer:
Butoxors [25]2 years ago
6 0

<em>Given - a+b+c = 0</em>

<em>To prove that- </em>

<em>a²/bc + b²/ac + c²/ab = 3</em>

<em>Now we know that</em>

<em>when x+y+z = 0,</em>

<em>then x³+y³+z³ = 3xyz</em>

<em>that means</em>

<em> (x³+y³+z³)/xyz = 3 ---- eq 1)</em>

<em>Lets solve for LHS</em>

<em>LHS = a²/bc + b²/ac + c²/ab</em>

<em>we can write it as LHS = a³/abc + b³/abc + c</em><em>³</em><em>/abc</em>

<em>by multiplying missing denominators,</em>

<em>now take common abc from denominator and you'll get,</em>

<em>LHS = (a³+b³+c³)/abc --- eq (2)</em>

<em>Comparing one and two we can say that</em>

<em>(a³+b³+c³)/abc = 3</em>

<em>Hence proved,</em>

<em>a²/bc + b²/ac + c²/ab = 3</em>

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Answer:

Step-by-step explanation:

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3 years ago
Why do interest rates on loans tend to be higher in a strong economy than in a weak one?
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the answer is A.

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8 0
3 years ago
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The car would be worth $16,000 after 5 years.
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3 years ago
Find the value of x. if necessary, round to the nearest tenth a=47sq in
kipiarov [429]

the picture in the attached figure


we know that

area of the triangle is equal to

A=(b*h)/2


in this problem

A=47 in²

b=x

h=x

so

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What is the actual distance between these streets?
scoundrel [369]

It's D 4 3/8 miles

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Hope this helps!

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