Question

The difference between Squares of two
numbers is 120. The square of smaller number
is twice The greater number find those numbers​

Answer 1

${\huge{\tt{\underline{\underline{Question :}}}}}$

→ The difference between Squares of two

numbers is 120. The square of smaller number

is twice The greater number find those numbers

${ \huge{ \tt {\underline{ \underline{Answer :}}}}}$

→ Let us consider that the numbers are p and q with p > q .

→ Then , by the given conditions , Difference of the squares of p and q = 120

→ => p ? - q2 = 120.....( i )

→ And

→ Square of the smaller number = Twice the greater number

→ => q2 = 2p.....( ii )

→ Putting q2 = 2p in ( i ) , We get

→ p - 2p = 120

→ => p2-2p + 1 = 120 + 1

→ => ( p - 1 ) 2 = 121

→ => ( p - 1 ) 2 = 112

→ => p - 1 = † 11

→ => p = 1 + 11

→ Thus , we get

→ dp = 1 + 11

→ And

→ p = 1 - 11

→ p = 12 and p = -10

→ When , p = 12 , from ( ii ) , we get

→ q2 = 2 x 12

→ => q2 = 24

→ => q2 = 22 x 6

→ => q = + 2V6

→ Again , when p = -10 , from ( ii ) , we get

→ q2 = 2 × ( -10 )

→ => q2 = -20

→ => q2 = 22 x 5 xi ?

→ Where i = v ( -1 ) and i = -1

→ => q = + 2V5 i

→ Hence , the required numbers are ( 12 , +226 ) and ( -10 , † 215 i ) .

$\huge\tt{ \underline{ \underline {\pink{Note :}}}}$

→ For lower classes , only calculate the value of q with p = 12 only , because complex number i = V ( -1 ) may not be in syllabus .

Answer 2

Answer:

Two numbers are 12 and √24

Step-by-step explanation: Let us suppose the greater no. be x and smaller no. be y.

According to the question:-

x² -y² = 120......(1)

y² = 2x........(2)

x² - y² = 120

Putting the value of y² = 2x in equation (1)

x² - 2x = 120

x² - 2x - 120 =0

x² - 12x + 10x - 120 = 0

x(x - 12) + 10(x - 12) = 0

(x + 10)(x- 12) = 0

x + 10

x = -10 It will be neglectd positive can't be negative.

x - 12 = 0

x = 12

Putting value of x = 12 in equation (2)

y² = 2x

y² = 2 × 12

y² = 24

y = √24

Hence, Two numbers are 12 and √24.

              I hope it will be helpful.