Question

the number x is 2 more than the number y. If the sum of the squares of s and y is 34, find the product of x and y​

Answer 1

☯GIVEN :

• The number x is 2 more than the number y.

• The sum of the squares of x and y is 34.

☯TO FIND :

• The product of x and y.

☯FORMULA REQUIRED :

• $\bigstar \underline{ \boxed{ \pink{ \bf{ {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} }}}}$

➲SOLUTION :

• The number x is 2 more than the number y.

$\longrightarrow{ \sf{x =y + 2 }}$

$\longrightarrow{ \bf{x- y = 2 \:\:\:...(i)}}$

• The sum of the squares of x and y is 34.

$\longrightarrow{ \bf{x^2 +y ^2 =34 \:\:\: ..(ii)}}$

Squaring on both sides in (i) :

$\implies \sf{{(x - y)}^{2} = {(2)}^{2} }$

• Used $\bf{(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2}$ :

$\implies \sf{ {(x)}^{2} - 2 \times x \times y + {(y)}^{2} = 4 }$

$\implies \sf{ {x}^{2} - 2 x y + {y}^{2} = 4}$

$\implies \sf{ {x}^{2} + {y}^{2} - 2xy = 4}$

• Substituting the value of (ii) :

$\implies \sf{ 34 - 2xy = 4}$

$\implies \sf{ 34 - 4 = 2xy}$

$\implies \sf{ 30 = 2xy}$

$\implies \sf{ \cancel{\dfrac{30 }{2} } = xy}$

$\implies \sf{ 15 = xy}$

$\implies \underline{ \boxed{ \pink{\bf{ xy = 15} }}}$

$\huge{\green{\therefore}}$ The product of x and y is 15.