find the value of √3×√3
Answers
Answer:
[math]x=\sqrt{3+\sqrt{3+\sqrt{3+\cdots}}}[/math]
[math]x^2=3+\sqrt{3+\sqrt{3+\cdots}}[/math]
[math]x^2-3=\sqrt{3+\sqrt{3+\cdots}}[/math]
[math]x^2-3=x[/math]
[math]x^2-x-3=0[/math]
[math]x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(1)(-3)}}{2(1)}[/math]
[math]x=\dfrac{1\pm\sqrt{1+12}}{2}[/math]
[math]x=\dfrac{1\pm\sqrt{13}}{2}[/math]
Step-by-step explanation:
Answer:
Here's how it works.
There are two functions in maths which are complementary or opposite to each other, but in multiples.
Root and Power.
Root of a number is the value you get that when multiplied with itself gives the number.
Like for instance, a number X is divided into two equal parts, Y, such that when multiplied with each other once, they give X.
Y * Y = X.
You might think X can ve divided into two equal parts by dividing it by 2, but no. That is only for one case ever, that is for X = 4.
Let there be a X = 12. How do you divide it in two equal parts so that, when you multiply them you get 12?
What's that? 2 equal parts? 12 / 2 = 6 each? Nope.
6 * 6 = 36.
What to do?
Let's take the closest multiplication. 3 * 3. Gives 9. Close enough. 4 * 4. Gives 16. Okay you get the point. The answer is between 3 and 4. Now, 12 is 4 figures away from 16 and 3 from 9. So the answer lies between 3 and 3.5, so we check 3.5 and get 12.25. So we know its between 3.4 and 3.5, and we go on.
Now, what is a Power? Or it is also known as an exponent.
When you multiply the same number by itself by one, it is said to raise the power of that number by one.
Just imagine, there are 11 people on a team, and 11 on another. The overall power (quantity) is equal here. What if someone joins team A and makes it 12? The power of that team increases by one.
But this doesn't apply to math. 11 + 1 doesn't account for an additional of power to it, but 11 * 11 does it.
Let's take a fight. One fighter against one. Fair. Two fighters against one. Unfair. What happens here, is, if both fighters have X power, and another fighter joins team A, it will have 2X power, fair, but we can say X with power of 2. What if there are 3 against 2? Team A with X with power of 3 and B with X of power of 2.
So when you multiply two numbers, Y * Y to get an X, that number is said to be raised to the power, the number of times it is multiplied to itself.
Y has power 1. (Which is nothing but Y)
2Ys have power 2. (Which is nothing but Y * Y)
3Ys have power 3. (Which is nothing but Y * Y * Y)
.
.
.
And so on.
And when you reverse power, it becomes root.
That's it.