Question

If a+b=10 and ab=24 so find the value of a^3+b^3

Answer 1

Answer:

your answer attached in the photo

Answer 2

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Question :-

If ,

a + b = 10 & ab = 24

Find the value of a^3 + b^3 ?

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Given :-

If ,a + b = 10 & ab = 24

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Required to find :-

• Find the value of a^3 + b^3

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Explanation :-

On the question it is given that,

a + b = 10 & ab = 24

He asked us to find the value of a^3 + b^3 .

In order to find this value we have use first given information and by performing some funtions on it we can find the required value .

In every case we have to take the use of first hint .

Here , in this case the first hint is a + b = 10 .

Now , just see the value which is needed to be find only the power .

If the power is 2 we have to square the first hint .

Similarly, if the power is 3 we have to do cubing and so on .

In this case we have to do cubing .

when we do cubing we actually get the reduced form of an identity .

So, we have to expand it using that identity .

Hence, once expanded substitute the given values in it .

And by solving further we can find the value of a^3 + b^3 .

So, now let's crack the above question .

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Solution :-

Given :

➾ a + b = 10 & ab = 24

So,

Let's consider ,

➾ a + b = 10

Now do cubing on both sides

So,

➾ (a + b)^3

Now expand this according to the identity .

Hence,

➾ (a + b)^3 = a^3 + b^3 + 3ab(a + b )

As we know that,

➾ a + b = 10

&

➾ ab = 24

Now substitute this values instead of variables .

Hence,

➾ (10)^3 = a^3 + b^3 + 3 ( 24)(10)

➾ 1000 = a^3 + b^3 + 3(240)

➾ 1000 = a^3 + b^3 + 720

Now transpose 720 to the L.H.S. side .

We get,

➾ 1000 - 720 = a^3 + b^3

➾ 280 = a^3 + b^3

This can be written as,

➜ a^3 + b^3 = 280

$\underline{\boxed{\therefore{Value \; of \; {a}^{3} + {b}^{3} = 280 }}}$

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☑ Hence solved .

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