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Degger [83]
3 years ago
10

How to solve this equation involving radicals. 8x(x – 6)1/2 + 4(x – 6)3/2 = 0

Mathematics
1 answer:
Naya [18.7K]3 years ago
4 0
8x(x - 6)1/2 + 4(x - 6)3/2 = 0
8x(x) - 8x(6)1/2 + 4(x) - 4(6)3/2 = 0
8x² - 48x(1/2) + 4x - 24(3/2) = 0
8x² - 24x + 4x - 36 = 0
8x² - 20x - 36 = 0
x = <u>-(-20) +/- √((-20²) - 4(8)(-36))</u>
                        2(8)
x = <u>20 +/- √(400 + 1152)</u>
                  16
x =<u> 20 +/- √1552</u>
             16
x = <u>20 +/- √(16 × 97)</u>
                16
x = <u>20 +/- √16 √97
</u>               16<u>
</u>x = <u>20 +/- 4 √97
</u>              16
x = <u>20 +/- 4(9.848857802)</u>
                     16
x = <u>20 +/- 39.39543121</u>
                    16
x = <u>20 + 39.39543121</u>        x = <u>20 - 39.39543121</u>
                  16                                        16
x = <u>59.39543121</u>                x = <u>-19.39543121</u>
              16                                         16
x = 3.71221445                  x = -1.212214451
<u />
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==>   3 = <em>a</em> (<em>x</em> + 1) + <em>b</em> (<em>x</em> - 1)

==>   3 = (<em>a</em> + <em>b</em>) <em>x</em> + <em>a</em> - <em>b</em>

==>   <em>a</em> + <em>b</em> = 3 and <em>a</em> - <em>b</em> = 0

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