Question

Kuis ⁽¹⁴⁶⁾ Tentukan panjang AC dari segitiga ini

Answer 1

Jawaban:

[tex]ac = \frac{ \sqrt{413} }{14} [/tex]

Penjelasan dengan langkah-langkah:

[tex] \sqrt{ \sqrt{ {5}^{2} } - ac {}^{2} } + \sqrt{ \sqrt{3 {}^{2} } - ac {}^{2} } = \sqrt{7} [/tex]

[tex] \sqrt{5 - ac {}^{2} } + \sqrt{3 - ac {}^{2} } = \sqrt{7} [/tex]

[tex] \sqrt{5 - ac {}^{2} } = \sqrt{7} - \sqrt{3 - ac {}^{2} } [/tex]

[tex]( \sqrt{5 - ac {}^{2} }) {}^{2} = ( \sqrt{7} - \sqrt{3 - ac {}^{2} } ) {}^{2} [/tex]

[tex]5 - ac {}^{2} = 7 - 2 \sqrt{7(3 - ac {}^{2} )} + 3 - ac {}^{2} [/tex]

[tex]5 = 10 - 2 \sqrt{21 - 7ac {}^{2} } [/tex]

[tex]2 \sqrt{21 - 7ac {}^{2} } = 10 - 5[/tex]

[tex] \sqrt{21 - 7ac {}^{2} } = \frac{5}{2} [/tex]

[tex]21 - 7ac {}^{2} = \frac{25}{4} [/tex]

[tex] - 7ac {}^{2} = \frac{25}{4} - 21[/tex]

[tex] - 7ac {}^{2} = \frac{25}{4} - \frac{84}{4} [/tex]

[tex] - 7ac {}^{2} = - \frac{59}{4} [/tex]

[tex]ac {}^{2} = \frac{59}{28} [/tex]

[tex]ac = \sqrt{ \frac{59}{28} } [/tex]

[tex]ac = \sqrt{ \frac{413}{196} } [/tex]

[tex]ac = \frac{ \sqrt{413} }{14} [/tex]

#CMIIW

[tex]\boxed{\colorbox{ccddff}{Answered by Danial Alfat}}[/tex]