Math, asked by XxLUCYxX, 1 month ago

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Answered by Anonymous
5

Answer:

x = 13.15

Step-by-step explanation:

   \small{\longrightarrow  \dfrac{ \sqrt{x + 4}  +  \sqrt{x - 10} }{\sqrt{x + 4} -  \sqrt{x - 10}  }  =  \dfrac{5}{2} }

Applying componendo and dividendo, according to which if a/b = c/d , then (a+b)/(a-b) = (c+d)/(c-d)

 \small{ \longrightarrow  \dfrac{ (\sqrt{x + 4}  +  \sqrt{x - 10} ) +(\sqrt{x + 4} -  \sqrt{x - 10} ) }{(\sqrt{x + 4}  +  \sqrt{x - 10})  - (\sqrt{x + 4} -  \sqrt{x - 10}  )}  =  \dfrac{5 + 2}{5 - 2} }

 \small{ \longrightarrow  \dfrac{ \sqrt{x + 4}  +  \sqrt{x - 10}  +\sqrt{x + 4} -  \sqrt{x - 10}  }{\sqrt{x + 4}  +  \sqrt{x - 10}  - \sqrt{x + 4}  +  \sqrt{x - 10}  }  =  \dfrac{7}{3} }

 \small{ \longrightarrow  \dfrac{ 2\sqrt{x + 4} }{ 2 \sqrt{x - 10}  }  =  \dfrac{7}{3} }

 \small{ \longrightarrow  \dfrac{ \not 2\sqrt{x + 4} }{ \not 2 \sqrt{x - 10}  }  =  \dfrac{7}{3} }

 \small{ \longrightarrow  \dfrac{ \sqrt{x + 4} }{  \sqrt{x - 10}  }  =  \dfrac{7}{3} }

Squaring both sides, we get :

 \small{ \longrightarrow   \left(\dfrac{ \sqrt{x + 4} }{  \sqrt{x - 10}  } \right)^{2}   = \left(  \dfrac{7}{3} \right)^{2}  }

 \small{ \longrightarrow\dfrac{ x + 4}{x - 10}   =  \dfrac{49}{9}   }

Now, cross multiply :

 \small{ \longrightarrow9( x + 4)= 49(x - 10)}

 \small{ \longrightarrow9x + 36= 49x - 490}

 \small{ \longrightarrow  36 + 490= 49x  - 9x}

 \small{ \longrightarrow  526= 40x}

 \small{ \longrightarrow   \dfrac{526}{40}= x}

 \small{ \longrightarrow   \dfrac{263}{20}= x}

 \small{ \longrightarrow   13.15= x}

Hence this is the required value of x.

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