Question

given (x -y)= 5 and xy = 36, find the value of x2 + y2​

Answer 1

Answer:

Hence the value of x^2+y^2=97

Step-by-step explanation:

(x-y)=5

(x-y)^2=25

xy=36

(x-y)^2=x^2+y^2-2xy

x^2+y^2=(x-y)^2+2xy

=25+(2×36)

=25+72

=97

Answer 2

Given: $(x -y)= 5 \ and\ xy = 36$.

We have to find the value of$x^{2} + y^{2}$.

As we know that the identity is:$(a-b)^{2} =a^{2} -2ab+b^{2}$

We are solving in the following way:

We have,

$(x -y)= 5 \ and\ xy = 36$

From identity we can say that,

$(x-y)^{2} =x^{2} -2xy+y^{2}$

Now by putting the given values in the above equtaion we get,

$\Rightarrow (5)^{2} =x^{2} +y^{2} -2\times36\\\Rightarrow 25=x^{2} +y^{2}-72\\\Rightarrow x^{2} +y^{2}=25+72\\\Rightarrow x^{2} +y^{2} = 97$

Hence, the value of $x^{2} + y^{2}$will be$97$.