Question

The difference between the square of two number is 384 if bigger number is 5 times the smaller number find the both numbers?

Answer 1

Step-by-step explanation:

LET the 1st no, be x

             2nd no.be 5x (given ATQs)

the equation forms:

5x^2 - x^2 = 384

4x^2=384

x^2=384/4

x =+-$\sqrt{96}$

x=$+4\sqrt{6} ,-4\sqrt{6}$

therefore, 5x =$20\sqrt{6} ,-20\sqrt{6}$

we got the no. mark the best

Answer 2

Given :

• difference of square of 2 numbers = 384

$\large \red{ \underline{ \underline{ \green{ \rm \: solution : }}}}$

$\rightarrow$ let the smaller number be = x

$\therefore$ bigger number = 5 × x = 5x

• According to question :

$\bigstar$ difference of square of 2 numbers = 384

$\implies$ (x)² - (5x)² = 384

$\implies$ x² - 25x² = 384

$\implies$ - 24x² = 384

$\: \: \: \: \: \: \: \: \rightarrow\pink{ \underline{ \orange{ \rm \: on \: transposing \: the \: terms : }}}$

$\implies \rm{x}^{2} = \large \frac{384}{24}$

$\implies$ x² = 16

$\implies \red{ \rm {x} = \sqrt{16} }$

$\therefore$ x = 4

$\rightarrow \purple{\rm \: smaller \: number = x = } \: \green{ \underline{ 4}}$

$\rightarrow \pink{\rm \: bigger \: number = x \times 5 }$

= 4 × 5

$\therefore \purple{\rm \: bigger \: number = \green{ \underline{ 20}}}$

• Check :

(x)² - (5x)² = 384

$\bigstar$ here,

• x = 4

$\implies$ 4² - (4 × 5)² = 384

$\implies$ 16 - 20² = 384

$\implies$ 16 - 400 = 384

$\large \red{384 = 384}$

L.H.S = R.H.S

Hence proved