Question: "For Exercise, solve the equations and inequalities. Write..."

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

Dottie Parra

Answered question

2021-10-04

For Exercise, solve the equations and inequalities. Write the solution sets to the inequalities in interval notation.

{(x^{2} - 9)}^{2} - 2 (x^{2} - 9) - 35 = 0

Answer & Explanation

Benedict

Skilled2021-10-05Added 108 answers

Now, Solving the equation
${(x^{2} - 9)}^{2} - 2 (x^{2} - 9) - 35 = 0 {∵ {(a - b)}^{2} = a^{2} - 2 a b + b^{2}}$
$x^{4} + 81 - 18 x^{2} - 2 x^{2} + 18 - 35 = 0$
$x^{4} - 20 x^{2} + 64 = 0$
Let $t = x^{2}$
Then,
$t^{2} - 20 t + 64 = 0$
$t^{2} - (16 + 4) t + 64 = 0$
$t^{2} - 16 t - 4 t + 64 = 0$
$t (t - 16) - 4 (t - 16) = 0$
$(t - 16) (t - 4) = 0$
$t = 16$ and $t = 4$
Now, Substitute $t = x^{2}$
So, $x^{2} = 16$ and $x^{2} = 4$
$x = \pm 4$ and $x = \pm 2$
Answer: Hence, the values of x are
$x = 4, x = - 4, x = 2$ and $x = - 2$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Pre-Algebra

Which expression has both 8 and n as factors???
One number is 2 more than 3 times another. Their sum is 22. Find the numbers
8, 14
5, 17
2, 20
4, 18
10, 12
Perform the indicated operation and simplify the result. Leave your answer in factored form
$[\frac{(4 x - 8)}{(- 3 x)}] . [\frac{12}{(12 - 6 x)}]$
An ordered pair set is referred to as a ___?
Please, can u convert 3.16 (6 repeating) to fraction.
Write an algebraic expression for the statement '6 less than the quotient of x divided by 3 equals 2'.
A) $6 - \frac{x}{3} = 2$
B) $\frac{x}{3} - 6 = 2$
C) 3x−6=2
D) $\frac{3}{x} - 6 = 2$
Find: $2.48 \div 4$ .
Multiplication $999 \times 999$ equals.
Solve: (128÷32)÷(−4)=
A) -1
B) 2
C) -4
D) -3
What is $0.78888 ... . .$ converted into a fraction? $(0.7 \bar{8})$
The mixed fraction representation of 7/3 is...
How to write the algebraic expression given: the quotient of 5 plus d and 12 minus w?
Express 200+30+5+4100+71000 as a decimal number and find its hundredths digit.
A)235.47,7
B)235.047,4
C)235.47,4
D)234.057,7
Find four equivalent fractions of the given fraction: $\frac{6}{12}$
How to find the greatest common factor of $80 x^{3}, 30 y x^{2}$ ?

Didn't find what you were looking for?