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2 years ago

3x^2 + 2x + 5 = 0

Mathematics

1 answer:

Lyrx [107]2 years ago

3 0

Answer:

Step-by-step explanation:

3x2−2x−5=0

Let us factorize using the split the middle term method.

On inspection we observe that middle term can be split in two parts whose product is equal to the product of first and third term.

Two terms are −5xand3x

The equation becomes

3x2+3x−5x−5=0, pairing the two and taking out common factors

⇒(3x2+3x)−(5x+5)=0,

don't forget to change the sign of −5 once placed inside the parenthesis.

⇒3x(x+1)−5(x+1)=0

⇒(x+1)(3x−5)=0

Either (x+1)=0 or (3x−5)=0

We obtain x=−1,53

or x=−1,123

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Answer:

49.73

Step-by-step explanation:

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3 years ago

Read 2 more answers

Prove the following by induction. In each case, n is apositive integer.<br> 2^n ≤ 2^n+1 - 2^n-1 -1.

frutty [35]

<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

$2^n\leq 2^{n+1}-2^{n-1}-1$

where n is a positive integer.

Let us take n=1

then we have:

$2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2$

Hence, the result is true for n=1.

Let us assume that the result is true for n=k

i.e.

$2^k\leq 2^{k+1}-2^{k-1}-1$

Now, we have to prove the result for n=k+1

i.e.

<u>To prove:</u> $2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Let us take n=k+1

Hence, we have:

$2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)$

( Since, the result was true for n=k )

Hence, we have:

$2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2$

Also, we know that:

$-2$

(

Since, for n=k+1 being a positive integer we have:

$2^{(k+1)+1}-2^{(k+1)-1}>0$ )

Hence, we have finally,

$2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Hence, the result holds true for n=k+1

Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

$2^n\leq 2^{n+1}-2^{n-1}-1$ where n is a positive integer.

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3 years ago

Which expression is equivalent to 7a^3(6a^2+a^2)-4a^6?

Thepotemich [5.8K]

Simply simplify:

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3 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

Please help me it is very much appreciated

pshichka [43]

Hope it helps you!

-miraculousfanx-

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