Answer:
A) x = 5 or x = 6
B) x = 0.298 or 6.702
C) x = 3
D) x = ±1
Step-by-step explanation:
A) Values of x for which;
x² − 11x + 31 = 1
x² - 11x + 30 = 0
Using quadratic formula, we have;
x = 5 and x = 6
B) Values of x for which;
x² − 5x − 3 = 2x − 5
x² − 5x - 2x - 3 + 5 = 0
x² - 7x + 2 = 0
Using quadratic formula, we have;
x = 0.298 or 6.702
C) Values of x for which;
7x + 1 = 3x² − 2x + 1
3x² - 2x - 7x + 1 - 1 = 0
3x² - 9x = 0
3x² = 9x
Divide both sides by 3x to get;
x = 3
D) Values of x for which;
−2x² + 5x + 6 = 4x² + 5x
Rearranging, we have;
4x² + 2x² + 5x - 5x - 6 = 0
6x² - 6 = 0
x² = 6/6
x² = 1
x = √1
x = ±1
The values of [tex]x[/tex] for the given situations would be as follows:
A). [tex]x = 5[/tex] or [tex]x = 6[/tex].
B). [tex]x = 0.298[/tex] or [tex]6.702[/tex]
C). [tex]x = 3[/tex]
D). [tex]x =[/tex] ±[tex]1[/tex]
a). [tex]x^2 - 11x + 31 = 1[/tex]
⇒ [tex]x^2 - 11x + 30 = 0[/tex]
by employing the quadratic equation, we have the values of [tex]x[/tex];
Considering
a = 1
b = -11
c = 30
⇒ {[tex]-(-11)[/tex] ± [tex]\sqrt{(-11)^2 -4 .1. 30 }[/tex]}[tex]/2.1[/tex]
Now,
[tex]x =[/tex] ([tex]11[/tex] ± [tex]1)/2[/tex]
Thus, the values for which the given trinomial would be equivalent to 1 would be:
∵ [tex]x = 5[/tex] and [tex]x = 6[/tex]
b). [tex]x^2 - 5x - 3 = 2x - 5[/tex]
⇒ [tex]x^2 - 5x - 2x - 3 + 5 = 0[/tex]
⇒ [tex]x^2 - 7x + 2 = 0[/tex]
by employing the quadratic equation, we have the values of [tex]x[/tex];
Therefore, the values of polynomials [tex]x^2 - 5x - 3 = 2x - 5[/tex] when:
∵ [tex]x = 0.298[/tex] or [tex]x = 6.702[/tex]
c). [tex]7x + 1 = 3x^2 - 2x + 1[/tex]
⇒ [tex]3x^2 - 2x - 7x + 1 - 1 = 0[/tex]
⇒ [tex]3x^2 - 9x = 0[/tex]
⇒ [tex]3x^2 = 9x[/tex]
by dividing both the sides by [tex]3x[/tex] to receive;
Hence, the binomial and trinomial [tex]7x + 1 = 3x^2 - 2x + 1[/tex] when:
∵ [tex]x = 3[/tex]
d). [tex]-2x^2 + 5x + 6 = 4x^2 + 5x[/tex]
by arranging them again, we get;
[tex]4x^2 + 2x^2 + 5x - 5x - 6 = 0[/tex]
⇒ [tex]6x^2 - 6 = 0[/tex]
⇒ [tex]x^2 = 6/6[/tex]
The trinomial and binomial [tex]-2x^2 + 5x + 6 = 4x^2 + 5x[/tex] would be when:
∵ [tex]x =[/tex] ±[tex]1[/tex]
Learn more about "Binomial" here:
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