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myrzilka [38]
2 years ago
15

The sum of two numbers is equal to 11 and the difference is 19. What are the two numbers?

Mathematics
1 answer:
charle [14.2K]2 years ago
5 0

\bold{\huge{\pink{\underline{ Solution }}}}

<u>We </u><u>have </u><u>given </u><u>in </u><u>the </u><u>question </u><u>that</u><u>, </u>

  • <u>The </u><u>sum </u><u>of </u><u>2</u><u> </u><u>numbers </u><u>is </u><u>equal </u><u>to </u><u>1</u><u>1</u><u> </u>
  • <u>The </u><u>difference </u><u>between </u><u>two </u><u>numbers </u><u>is </u><u>1</u><u>9</u><u> </u><u>.</u>

\bold{\underline{ To \: Find }}

  • <u>We </u><u>have </u><u>to </u><u>find </u><u>the </u><u>value </u><u>of </u><u>x </u><u>and </u><u>y</u><u>. </u>

\bold{\underline{ Let's \: Begin }}

Let the two numbers be x and y

<u>According </u><u>to </u><u>the </u><u>question</u><u>, </u>

\sf{ x + y = 11......eq(1) }

\sf{ x - y = 19......eq(2) }

<u>Solving </u><u>eq(</u><u> </u><u>1</u><u> </u><u>)</u><u> </u><u>we </u><u>get </u><u>:</u><u>-</u><u> </u>

\sf{ x + y = 11  }

\sf{ x = 11 - y ......eq(3 ) }

<u>Subsituting </u><u>eq(</u><u>3</u><u> </u><u>)</u><u> </u><u>in </u><u>eq</u><u>(</u><u>2</u><u>)</u><u> </u><u>:</u><u>-</u>

\sf{ x - y = 19 }

\sf{ ( 11 - y) - y = 19 }

\sf{ 11 - y - y = 19 }

\sf{  11 - 2y = 19 }

\sf{ - 2y = 19 - 11  }

\sf{ - 2y = 8}

\sf{ y = 8/(-2) }

\sf{ y = - 4 }

\sf{\red{Thus ,\: the\: value\: of \: y = -4}}

<u>Now</u><u>, </u><u> </u><u>Subsitute </u><u>the </u><u>value </u><u>of </u><u>y </u><u>in </u><u>eq(</u><u> </u><u>3</u><u> </u><u>)</u><u> </u><u>:</u><u>-</u>

\sf{ x = 11 - y  }

\sf{ x = 11 - (-4 )  }

\sf{ x = 11 + 4  }

\sf{ x = 15 }

Hence, The value of x and y are 15 and (-4) .

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Step-by-step explanation:

The question is poorly formatted. The original question is:

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7

We have:

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7

Open bracket

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =(8^ \frac{2}{3} *x^{3* \frac{2}{3}}) \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =(8^ \frac{2}{3} *x^2) \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}

Express 8 as 2^3

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =(2^{3* \frac{2}{3}} *x^2) \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =(2^2 *x^2) \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7} =4x^2 \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}

Express 2^3 as 8

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}=4x^2 \sqrt{75x^3} + 8\sqrt{ 3x^7}

Expand each exponent

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}=4x^2 \sqrt{25x^2 *3x} + 8\sqrt{ 3x * x^6}

Split

(8x^3)^ \frac{2}{3} \sqrt{75x^3} + 2^3 \sqrt{ 3x^7}=4x^2 \sqrt{25x^2} *\sqrt{3x} + 8\sqrt{3x} * \sqrt{x^6}

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Factorize

(8x^3)^ \frac{2}{3} \sqrt{75x^3}  + 2^3 \sqrt{ 3x^7} =28x^3\sqrt{3x}

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