if-a-2-2-4a-find-5a-4-16-5a-4-

Question Number 201931 by hardmath last updated on 15/Dec/23

if {(a - 2)}^{2} = 4 a

find : 5 a + 4 + \frac{16}{5 a + 4} = ?

Answered by mr W last updated on 16/Dec/23

a^{2} - 4 a + 4 = 4 a

a^{2} - 8 a + 4 = 0

{(a - 4)}^{2} = 12

a = 4 \pm 2 \sqrt{3}

5 a + 4 = 24 \pm 10 \sqrt{3}

\frac{16}{5 a + 4} = \frac{16}{24 \pm 10 \sqrt{3}} = 96 \mp 40 \sqrt{3})

5 a + 4 + \frac{16}{5 a + 4} = 24 \pm 10 \sqrt{3} + 96 \mp 40 \sqrt{3})

= 30 (4 \pm \sqrt{3})

Commented by hardmath last updated on 16/Dec/23

cool dear professor thankyou