State true or false.
If $(4 a + 9 b) (4 c - 9 d) = (4 a - 9 b) (4 c + 9 d)$ , then $a : b = c : d$ .

True

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

False

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A True
Given,

$(4 a + 9 b) (4 c - 9 d) = (4 a - 9 b) (4 c + 9 d)$

$16 a c - 36 a d + 36 b c - 81 b d = 16 a c + 36 a d - 36 b c - 81 b d$

$16 a c - 36 a d = - 72 b c + 16 a c + 36 a d$

$- 72 a d = - 72 b c$

$a d = b c$

$\Rightarrow \frac{a}{b} = \frac{c}{d}$

$∴ a : b = c : d$

Suggest Corrections

Similar questions

64 a^{3} - 27 b^{3} - 144 a^{2} b + 108 a b^{2}

= (4 a - 3 b) (4 a - 3 b) (4 a - 3 b)

\frac{{cos}^{4} A}{{cos}^{2} B} + \frac{{sin}^{4} A}{{sin}^{2} B} = 1

{sin}^{4} A + {sin}^{4} B = 2 {sin}^{2} A {sin}^{2} B

3 a - 4 b + 3 c

- 4 a + 5 b - 6 c

4 a - 7 b + 6 c

If A:B = $\frac{1}{2} : \frac{3}{8}$ , B:C = $\frac{1}{3} : \frac{5}{9}$ and C:D = $\frac{5}{6} : \frac{3}{4}$ , then the ratio A:B:C:D is

Join BYJU'S Learning Program