Asked by Kaur
Class 8 question
Find the value of x using quadratic formula
16x^4- 28x² - 8=0
Find the value of x using quadratic formula
16x^4- 28x² - 8=0
Answers
Answered by
Bosnian
Substitute x² with t
16 x⁴ - 28 x² - 8 = 0
become
16 t² - 28 t - 8 = 0
Divide both sides by 4
4 t² - 7 t - 2 = 0
The coefficients are:
a = 4 , b = - 7 , c = - 2
t1/2 = [ - b ± √ ( b² - 4 a c ) ] / 2 a =
[ - ( - 7 ) ± √ ( ( - 7 )² - 4 ∙ 4 ∙ ( - 2 ) ) ] / 2 ∙ 4 =
[ 7 ± √ ( 49 + 32 ) ] / 8 = ( 7 ± √81 ) / 8 = ( 7 ± 9 ) / 8
t1 = ( 7 + 9 ) / 8 = 16 / 8 = 2
t2 = ( 7 - 9 ) / 8 = - 2 / 8 = - 1 / 4
If x² = t
then
x = ± √ t
t1 = 2
x = ± √2
t2 = - 1 / 4
x = ± √ -1 / √4 = ± i / 2
The solutions are:
x = - i / 2 , x = i / 2 , x = -√2 , x = -√2
16 x⁴ - 28 x² - 8 = 0
become
16 t² - 28 t - 8 = 0
Divide both sides by 4
4 t² - 7 t - 2 = 0
The coefficients are:
a = 4 , b = - 7 , c = - 2
t1/2 = [ - b ± √ ( b² - 4 a c ) ] / 2 a =
[ - ( - 7 ) ± √ ( ( - 7 )² - 4 ∙ 4 ∙ ( - 2 ) ) ] / 2 ∙ 4 =
[ 7 ± √ ( 49 + 32 ) ] / 8 = ( 7 ± √81 ) / 8 = ( 7 ± 9 ) / 8
t1 = ( 7 + 9 ) / 8 = 16 / 8 = 2
t2 = ( 7 - 9 ) / 8 = - 2 / 8 = - 1 / 4
If x² = t
then
x = ± √ t
t1 = 2
x = ± √2
t2 = - 1 / 4
x = ± √ -1 / √4 = ± i / 2
The solutions are:
x = - i / 2 , x = i / 2 , x = -√2 , x = -√2
Answered by
Bosnian
The solutions are:
x = - i / 2 , x = i / 2 , x = -√2 , x = √2
x = - i / 2 , x = i / 2 , x = -√2 , x = √2
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