Question

if (x-y) = 5, xy = 4 then find (x² + y²)​

Answer 1

Answer:

Given:-

If ( x - y ) = 5, xy = 4 then find ( x² + y² ).

To Find:-

The value of ( x² + y² ).

Note:-

●》Here; for finding ( x² + y² ), we will use the formula of ( a - b )² i.e. ( a - b )² = a² + b² - 2ab. After that we will transpose the known terms to find ( x² + y² ).

●》Transposing - For finding unknown value, known value needs to be transposed from its side to another and also signs are changed in this process. For example - Negative becomes Positive.

Solution:-

$\huge\red{( x - y ) = 5, xy = 4}$

$\huge\red{ \ \ \ \ The \ \ value \ \ of \ \ ( x² + y² ) = ?}$

☆ According to note first point ( a = x, b = y )~

▪︎$( x - y )² = x² + y² - 2xy$

☆ Applying ( x - y ) and xy value~

▪︎$( 5 )² = x² + y² - 2 × 4$

▪︎$5 × 5 = x² + y² - 8$

▪︎$25 = x² + y² - 8$

☆ According to note second point ( Transposing )~

▪︎$25 + 8 = x² + y²$

▪︎$33 = x² + y²$

▪︎$x² + y² = 33$

$\huge\pink{The \ \ value \ \ of \ \ ( x² + y² ) = 33}$

Checking:-

♤ Let's check for ( x² + y² ) that Left hand side value = Right hand side value or not~

• $( x - y )² = x² + y² - 2xy \implies ?$

♤ Applying ( x - y ), xy, ( x² + y² ) values~

• $( 5 )² = 33 - 2 × 4 \implies ?$

• $5 × 5 = 33 - 8 \implies ?$

• $25 = 25 \implies ✔$

$\huge\green{Hence, Proved : ( x² + y² ) = 33}$

Answer:-

Hence, the value of ( x² + y² ) = 33.

:)