Question

if a equal to 3 + 2 root 2 find the value of a square + 1 by a square and a cube + 1 by a cube

Answer 1

.............. ..........

Answer 2

Answer:

Step-by-step explanation:

Concept:

A number can be obtained by multiplying the square root of that integer by itself. The word "square root" is represented by the symbol "sqrt"—square root of, end square root. The opposite of squaring an integer is finding its square root.

Any integer's square root equals that same number, which, when squared, yields the original number.

Let's assume that m is a positive integer, and that $\sqrt{} (m .m)= m2=m.$

A square root function is a one-to-one function in mathematics that receives a positive number as an input and outputs the square root of that number.

$f(x) = \sqrt{x}$

For instance, if$x=4$, the function output value is returned as $2$.

The other number that, when multiplied by itself a predetermined number of times, equals $x$ is  the root of the number $x$.

For instance, the third root of $64$, often known as the cube root, is $4$, since $64$ is equal to three times three fours multiplied together:

$4 * 4 * 4 = 64$

The above would be written as,

$\sqrt[3]{64} =4$

"the third root of $64$ is $4$" or "the cube root of $64$ is $4$" when spoken.

• Typically, the "cube root" is used to describe the third root of an integer.
• They are thus referred to as the $nth$ root, for instance the $5th$ root, $7th$ root, etc.

Given:

$a=3+2\sqrt{2}$

To find:

$a^{2} +\frac{1}{a^{2} } ,a^{3} +\frac{1}{a^{3} }$

Solution:

Given that $a=3+2\sqrt{2}$

$\frac{1}{a} =3-2\sqrt{2}$

$(a+\frac{1}{a} )^{2} =(3+2\sqrt{2} +3-2\sqrt{2} )^{2}$

$(a+\frac{1}{a})^{2} =(6)^{2}$

$(a+\frac{1}{a})^{2} =36$

$a^{2} +2*a*\frac{1}{a} +\frac{1}{a^{2} } =36$

$a^{2} +\frac{1}{a^{2} } =36-2$

$a^{2} +\frac{1}{a^{2} } =34$

$(a^{3} +\frac{1}{a^{3} }) =(a+\frac{1}{a} )(a^{2} +\frac{1}{a^{2} } -a*\frac{1}{a} )$

$(a^{3} +\frac{1}{a^{3} } )=6(34-1)$

$(a^{3} +\frac{1}{a^{3} } )=6*33$

$(a^{3}+\frac{1}{a^{3} })=198$

Hence $(a+\frac{1}{a^{2} } )=34$

           $(a^{3}+\frac{1}{a^{3} })=198$

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