Question

plz answer the question ​

Answer 1

⇒ Given Question:

If x - y = 13 and xy = 28, then find x² + y².

⇒ Algebraic Identity to be used:

→ (a - b)² = a² + b² - 2ab

⇒ Solution:

It is given that:

$\sf{x-y=13}$

So,

$\sf{x^2-y^2=13^2}$

$\sf{=(x-y)^2=13^2}$

This is in the form:

$\sf{(a-b)^2=a^2+b^2-2ab}$

Now, expanding the equation (x-y)² in the same way:

$\sf{=x^2+y^2-2xy=13^2}$

It is given that:

$\sf{xy=28}$

Now, substituting the known values in the equation,

$\sf{=x^2+y^2-2\times28=169}$

$\sf{=x^2+y^2-56=169}$

$\sf{x^2+y^2=169+56}$

$\sf{x^2+y^2=225}$

Hence, the value of x² + y² is 225.

Algebraic Identities:

   Algebraic identities is a set of rules regarding solving algebraic expressions where any constant can take the value of the variables a and b and the equation can be solved in that particular way. Given below is the chart of the algebraic identities:

$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\sf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\sf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\sf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\8)\sf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\\end{minipage}}$

Please refer the attachment to view the identities.