Question

The difference between squares of two numbers is 120. The square of smallernumber is twice the greater number. Find the numbers.
Urgent right answers only ^_^​

Answer 1

Answer

• The greater number = 12.
• The smaller number = √24 or -√24.

Given

• The difference between squares of two numbers is 120.
• The square of smaller number is twice the greater number.

To Do

• To find the numbers.

Step By Step Explanation

Assumption :

Let us consider the greater number be x and the square of smaller number be y.

So, the equation will be ⤵

$\longmapsto \sf {y}^{2} = 2x$

Now, the smaller number will be ⤵

$\longmapsto \sf {y}^{2} = 2x \\ \\ \longmapsto \sf y = \sqrt{2x}$

According to the Question :

The difference between squares of two numbers is 120.

Substituting the values :

$\longmapsto\sf {x}^{2} - {y}^{2}=120\\ \\ \longmapsto \sf {x}^{2} - { (\sqrt{2x}) }^{2} = 120 \\ \\\longmapsto \sf {x}^{2} - 2x = 120 \\ \\ \longmapsto \sf {x}^{2} - 2x - 120 = 0 \\ \\\longmapsto \sf {x}^{2} - 12x + 10x - 120 = 0 \\ \\\longmapsto \sf x(x - 12) + 10(x - 12) \\ \\\longmapsto \sf (x + 10)(x - 12) \\ \\\longmapsto \bf {\red{ x + 10 = 0 \implies \: x = - 10}} \\ \\\longmapsto \bf {\green{ x - 12 = 0 \implies \: x = 12}}$

But, the greater number could not be negative.

Therefore, the greater number = 12 and the smaller number = √2x => √24 or -√24.

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