Question

4. What should we added to 5x + 7xy +9y2 to obtain 9x² + 17xy + 19y2. jo iska sahi ans dega use 5 ⭐ mileage, or like bhi ans correct hona chahiye​

Answer 1

Answer:

9x²+17xy+19y2

Step-by-step explanation:

5x²+7xy+9y2

Solution:

• (5x²)

Answer 2

Given :

Polynomials -

• $\sf\:5x+7xy+9y^{2}$

• $\sf\:9x^{2}+17xy+19y^{2}$

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To find :

• The number which when added to $\sf\:5x+7xy+9y^{2}$ gives $\sf\:9x^{2}+17xy+19y^{2}$

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Assumption :

Let the number to be added be a.

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Solution :

According to the question -

$\sf\:5x+7xy+9y^{2} + a$ = $\sf\:9x^{2}+17xy+19y^{2}$

$\sf\to\:5x+7xy+9y^{2} +a = 9x^{2}+17xy+19y^{2}$

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Transposing +5x to RHS it becomes -5x

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$\sf\to\:+7xy+9y^{2} +a = 9x^{2}-5x+17xy+19y^{2}$

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Transposing +7xy to RHS it becomes -7xy

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$\sf\to\:+9y^{2} +a = 9x^{2}-5x+17xy-7xy+19y^{2}$

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Transposing 9y² to RHS it becomes -9y²

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$\sf\to\: a = 9x^{2}-5x+17xy-7xy+19y^{2}-9y^{2}$

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Carrying out some calculation at RHS

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$\sf\to\: a = 9x^{2}-5x+10xy+19y^{2} -9y^{2}$

$\sf\color{orange}{\to\: a = 9x^{2}-5x+10xy+10y^{2}}$ $\sf\color{black}{⋆}$

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Verification :

Let's add the value of a with $\sf\:5x+7xy+9y^{2}$ and check whether we will get $\sf\:9x^{2}+17xy+19y^{2}$ or not.

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‎$\sf\:5x+7xy+9y^{2}+a=9x^{2}+17xy+19y^{2}$

Taking LHS

‎$\sf\leadsto\:5x+7xy+9y^{2}+a$

Substituting the value of a

‎$\sf\leadsto\:5x+7xy+9y^{2}+9x^{2}-5x+10xy+10y^{2}$

Arranging the like terms together

‎$\sf\leadsto\:5x-5x+7xy+10xy+9y^{2}+10y^{2}+9x^{2}$

Proceeding with simple calculation

‎$\sf\leadsto\:\cancel{5x}-\cancel{5x}+17xy+19y^{2}+9x^{2}$

‎$\sf\leadsto\:17xy+19y^{2}+9x^{2}$

‎$\sf\leadsto\:9x^{2}+17xy+19y^{2}$

Hence Verified !~

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Required number is -

⠀⠀⠀⠀⠀⠀➻ $\bf\:9x^{2}-5x+10xy+10y^{2}$

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