The real solution of the equation 0.1 x 4 − 2.4 x 2 = 3.6 and check the solution. The solution of the given equation is x = ± 5.041 . Calculation: Consider the provided equation, 0.1 x 4 − 2.4 x 2 = 3.6 Write this equation in the standard form, 0.1 x 4 − 2.4 x 2 − 3.6 = 0 Apply the quadratic formula x = − b ± b 2 − 4 a c 2 a , x 2 = − − 2.4 ± − 2.4 2 − 4 0.1 − 3.6 2 0.1 = 2.4 ± 7.2 0.2 For the real values of x , take only the positive value of x 2 , x 2 = 2.4 + 7.2 0.2 Therefore, the value of x is x = ± 2.4 + 7.2 0.2 = ± 5.041 Check: First put x = 5.041 , 0.1 5.041 4 − 2.4 5.041 2 = ? 3.6 64.575 − 60.988 = ? 3.6 3.6 = 3.6 Which is true. Now, put x = − 5.041 , 0.1 − 5.041 4 − 2.4 − 5.041 2 = ? 3.6 64.575 − 60.988 = ? 3.6 3.6 = 3.6 Which is true. Hence, the solution of given equation is x = ± 5.041 .
The real solution of the equation 0.1 x 4 − 2.4 x 2 = 3.6 and check the solution. The solution of the given equation is x = ± 5.041 . Calculation: Consider the provided equation, 0.1 x 4 − 2.4 x 2 = 3.6 Write this equation in the standard form, 0.1 x 4 − 2.4 x 2 − 3.6 = 0 Apply the quadratic formula x = − b ± b 2 − 4 a c 2 a , x 2 = − − 2.4 ± − 2.4 2 − 4 0.1 − 3.6 2 0.1 = 2.4 ± 7.2 0.2 For the real values of x , take only the positive value of x 2 , x 2 = 2.4 + 7.2 0.2 Therefore, the value of x is x = ± 2.4 + 7.2 0.2 = ± 5.041 Check: First put x = 5.041 , 0.1 5.041 4 − 2.4 5.041 2 = ? 3.6 64.575 − 60.988 = ? 3.6 3.6 = 3.6 Which is true. Now, put x = − 5.041 , 0.1 − 5.041 4 − 2.4 − 5.041 2 = ? 3.6 64.575 − 60.988 = ? 3.6 3.6 = 3.6 Which is true. Hence, the solution of given equation is x = ± 5.041 .
Solution Summary: The author calculates the real solution of the equation 0.1x4-2.42=3.6 and checks the solution.
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
Chapter 1.6, Problem 76E
To determine
To calculate: The real solution of the equation 0.1x4−2.4x2=3.6 and check the solution.
The solution of the given equation is x=±5.041.
Calculation:
Consider the provided equation,
0.1x4−2.4x2=3.6
Write this equation in the standard form,
0.1x4−2.4x2−3.6=0
Apply the quadratic formulax=−b±b2−4ac2a,
x2=−−2.4±−2.42−40.1−3.620.1=2.4±7.20.2
For the real values of x, take only the positive value of x2,
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