Question

pls answer fast friends ​

Answer 1

GIVEN:

☛ a² + 1/a² = 34

TO FIND:

☛ a - 1/a

SOLUTION:

==> a² + 1/a² = 34

==> (a - 1/a)² - 2×a×1/a = 34

==> (a - 1/a)² = 34 + 2

==> (a - 1/a)² = 36

a - 1/a = 6, -6

Answer 2

4√2

Step-by-step explanation:

Given:

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

To find:

$\textsf{The value of}\:\:\:\: a - \dfrac{1}{a}$

What you have to do ?

1.Use Algebra Formula.

2. Substitute the given values.

3. Simplify and Get the answer.

Solution:

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

[Subtracting 2 from both side]

$a^2 + \dfrac{1}{{a}^{2}} - 2 = 34 - 2\\\\ a^2 + \dfrac{1}{{a}^{2}} - 2.a.\dfrac{1}{a}=32\\\\(a-\dfrac{1}{a})^2 = 32\\\\ a - \dfrac{1}{a} = \sqrt{32}\\\\a - \dfrac{1}{a} = 4\sqrt{2}$

Therefore, The required answer is 4√2.

Formula Used:

(a - b)² = a² - 2ab + b²

Some Important Algebra Formula

${(x + y)}^{2}={x}^{2}+{y}^{2}+2xy\\ \\{(x - y)}^{2}={x}^{2}+{y}^{2}-2xy\\ \\{(x+y)}^{2}= (x - y) {}^{2}+4xy\\ \\{(x-y)}^{2}=(x+y){}^{2}-4xy\\ \\ (x + y)^{2}+(x-y)^{2}=2( {x}^{2}+{y}^{2} )\\ \\(x+y)^{2}- (x-y) {}^{2}=4xy$