Question

If ( 13/4) whole to the power 4 - (13/3) whole to the power 4 ÷ ( 13/4)² - (13/3 )² = ( 13a÷12 )², find a.

Answer 1

$\frac{ (\frac{13}{4})^4 - (\frac{13}{3})^4 }{(\frac{13}{4})^2 - (\frac{13}{3})^2} \\ \\ = \frac{ [(\frac{13}{4})^2 + (\frac{13}{3})^2][(\frac{13}{4})^2 - (\frac{13}{3})^2] }{(\frac{13}{4})^2 - (\frac{13}{3})^2} \\ \\ = (\frac{13}{4})^2 + (\frac{13}{3})^2\\ \\ = [\frac{13}{4} +\frac{13}{3}]^2-2 \times \frac{13}{4} \times \frac{13}{3}\\ \\=[ \frac{13 \times 7}{12} ]^2-[ \frac{2 \times 13^2}{12} ]\\ \\=[ \frac{13 \times 7}{12} ]^2-[ \frac{2 \times 12 \times 13^2}{12^2} ]$

$=[ \frac{13}{12} ]^2(49-24)\\ \\ =[ \frac{13}{12} ]^2 \times 25\\ \\ =[ \frac{13 \times 5}{12} ]^2$

$Thus\ \boxed{ a=5}$

Answer 2

Answer:

Step-by-step explanation:

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