Question

the difference of two numbers is 4 and sum of their square is 26 find their product​

Answer 1

Question

• the difference of two numbers is 4 and sum of their square is 26 find their product.

Solution

_____________________________________

Given that,

• Difference between two numbers = 4
• Sum of their squares = 26

Let us assume the two numbers as x and y .

From this we get to know as,

• x - y = 4
• x² + y²= 26

We need to find the value of their product,

Hence, their product is xy.

The formula used is :-

$\small\sf\red{(x - y) {}^{2} = {x}^{2} + {y}^{2} - 2(xy)}$

Now, substitute the values in this formula.

We get as,

$\small\sf\red{(4) {}^{2} = 26 + 2(xy) }$

On solving we get as,

$\small\sf\red{16 = 26 + 2(xy)}$

On solving we get as,

$\small\sf\red{16 - 26 = 2(xy)}$

On solving we get as,

$\small\sf\red{ - 10 = 2(xy)}$

On solving we get as,

$\small\sf\red{ \frac{ - 10}{2} = xy}$

On solving we get as,

$\small\sf\red{ - 5 = xy}$

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Hence , the value of xy is -5

Answer 2

$\purple{\large\underline{\sf{Given- }}}$

The difference of two numbers is 4.

Sum of their square is 26.

$\pink{\large\underline{\sf{To\:Find - }}}$

The product of two numbers

$\green{\large\underline{\sf{Solution-}}}$

Let assume that

• First number is x

• Second number is y

• And further assume that x > y.

So,

According to statement,

The difference of two numbers is 4

$\rm :\longmapsto\:x - y = 4 - - - - (1)$

According to second condition

Sum of their squares is 26

$\rm :\longmapsto\: {x}^{2} + {y}^{2} = 26 - - - - (2)$

From equation (1), we have

$\rm :\longmapsto\:x - y = 4$

On squaring both sides, we get

$\rm :\longmapsto\: {(x - y)}^{2} = {4}^{2}$

$\rm :\longmapsto\: {x}^{2} + {y}^{2} - 2xy = 16$

$\rm :\longmapsto\: 26 - 2xy = 16$

$\red{ \bigg\{  \sf \: \because \: using \: equation \: (2) \bigg\}}$

$\rm :\longmapsto\:2xy = 26 - 16$

$\rm :\longmapsto\:2xy = 10$

$\bf\implies \:xy = 5$

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More Identities to know

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

(a + b)² = (a - b)² + 4ab

(a - b)² = (a + b)² - 4ab

(a + b)² + (a - b)² = 2(a² + b²)

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - b³ - 3ab(a - b)