Question

If (x+ y) = 5 and xy = 3 find the value of x² + y²​

Answer 1

Step-by-step explanation:

x + y = 5. xy= 3

(x+ y)² = 5² ( squaring both sides )

x² + y² + 2xy = 25

x² + y² + 2 × 3 = 25

x² + y² = 25 - 6

x²+ y² = 19

Answer 2

Answer:

Here, the concept of algebraic formulas has been used. We see that, we're given with two equations with their values and we're asked to calculate the value of another equation. We can calculate the other equation by using an algebraic formula and equating the values.

Formula used:

$\bullet\quad\boxed{\sf{{(a+b)}^{2}=}\bold{{a}^{2}+{b}^{2}+2ab}}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀

Here, we're provided with an equation, that is:

$\leadsto\sf{(x+y)=5}$

Squaring both the side, we get:

$\; \; \longrightarrow\quad\tt{{(x+y)}^{2}={5}^{2}}$

Using algebraic formula on LHS.

$\; \; \longrightarrow\quad\tt{{x}^{2}+{y}^{2}+2xy=25}$

In the question, it is given that:

$\qquad\qquad\leadsto\quad\sf{x.y=3}$

Using it in formula.

$\; \; \longrightarrow\quad\tt{{x}^{2}+{y}^{2}+2(3)=25}$

Performing multiplication.

$\; \; \longrightarrow\quad\tt{{x}^{2}+{y}^{2}+6=25}$

Transposing 6 from LHS to RHS. It's sign will get change.

$\; \; \longrightarrow\quad\tt{{x}^{2}+{y}^{2}=25-6}$

Performing subtraction.

$\; \; \longrightarrow\quad\underline{\boxed{\tt{{x}^{2}+{y}^{2}}=\bold{\purple{19}}}}$

Therefore, the required answer is:

⠀⠀⠀⠀⠀⠀❝ x² + y² = 19 ❞