Question

the difference of squares of two natural number is 45.the squares of the smaller number is 4 times the larger number. then the sum of numbers with formula method
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Answer 1

GIVEN :-

• The difference of squares of two natural number is 45.

• The square of the smaller number is 4 times the larger number.

TO FIND :-

• To find the sum of numbers.

SOLUTION :-

Let the numbers be x and y .

According to the first condition,

$\longrightarrow \sf x^2-y^2 = 45 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ............................(1)$

According to the second condition,

$\longrightarrow \sf y^2= 4x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ............................(2)$

Substitute y² = 4x in equation (1),

$\longrightarrow \sf x^2-4x= 45 \\\\\longrightarrow x^2- 4x = 45 \\\\\longrightarrow x^2-4x-45 = 0 \\\\\longrightarrow x^2-9x+5x- 45 = 0 \\\\\longrightarrow x(x-9)+5(x-9)= 0 \\\\\longrightarrow (x+5)(x-9)= 0 \\\\\longrightarrow \bf x = -5 \ , \ x = 9$

Negative number is not a natural number .

Value of x = 9

Substitute x = 9 in equation (2),

$\longrightarrow \sf y^2 = 4\times 9 \\\\\longrightarrow y^2 = 36\\\\\longrightarrow\bf y = 6$

The numbers are 9 and 6 .

Sum of numbers = 9 + 6 = 15