Question

Find the value of x²+y² when x+y =9 and xy= 18​

Answer 1

Answer:

↪ x² + y² = 45

Step-by-step explanation:

Given :-

x + y = 9

xy = 18

To Find :-

x² + y²

Solution :-

xy = 18

x + y = 9

↪(x+ y)² = 9² [ Squaring both sides ]

↪x² + 2xy + y² = 81

↪x² + y² = 81 - 2xy

↪x² + y² = 81 - 2 × 18

↪ x² + y² = 81 -36

↪ x² + y² = 45

Therefore,

↪ x² + y² = 45

Answer 2

Answer :-

• x² + y² = 45

Given :-

• The value of x² + y².

Solution :-

• Here the sum of x and y & product of x and y is given. We are asked to find the value of x² + y².

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We know that,

• (a + b)² = a² + 2ab + b²

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Where,

• a = x
• b = y

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Substituting the given values in this formula,

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$\bf \hookrightarrow {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}$

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$\bf \hookrightarrow {(9)}^{2} = {x}^{2} + 2(18) + {y}^{2}$

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$\bf \hookrightarrow 81 = {x}^{2} + 36 + {y}^{2}$

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$\bf \hookrightarrow {x}^{2} + {y}^{2} =81 - 36$

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$\bf \hookrightarrow \underline{\boxed{ \bf {x}^{2} + {y}^{2} = 45}}$

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Hence,

• The value of x² + y² is 45.

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