Question

If x+ 5 is the mean proportion between x+ 2 and x+ 9, then the value of x is.

a) 7
b) 5
c) 8​

Answer 1

Option (A) 7

Given,

• (x + 5) is the mean proportion between (x + 2) and (x + 9).

To Find,

• The values of x.

According to question,

Let, mean proportion between two numbers R and A is J. then a relation is occurred which is RA = J².

⇒ RA = J²

Here,

• R = (x + 2)
• A = (x + 9)
• J = (x + 5)

[ Put the values ]

⇒ (x + 2) (x + 9) = (x + 5)²

⇒ x(x + 9) + 2(x + 9) = x² + 10x + 25

⇒ x² + 9x + 2x + 18 = x² + 10x + 25

⇒ 11x + 18 = 10x + 25

⇒ 11x - 10x = 25 - 18

⇒ x = 7

Therefore,

The value of x is 7.

Answer 2

$\huge{\boxed{\rm{\red{Question}}}}$

If x+ 5 is the mean proportion between x + 2 and x + 9, then the value of x is –

• 7
• 5
• 8

$\huge{\boxed{\rm{\red{Answer}}}}$

${\bigstar}\large{\boxed{\sf{Given \: that}}}$

• x + 5 is the mean proportion between x + 2 and x + 9.

${\bigstar}\large{\boxed{\sf{To \: find}}}$

• Value of x.

${\bigstar}\large{\boxed{\sf{Solution}}}$

• Value of x = 7.

${\bigstar}\huge{\boxed{\boxed{\sf{Value \: of \: x \: is \: 7}}}}$

${\bigstar}\huge{\boxed{\boxed{\sf{Option \: a}}}}$

${\bigstar}\large{\boxed{\sf{Full \: solution}}}$

$\large\purple{\texttt{According to the question}}$

$\large\green{\texttt{Let proportional between 2 nos are ↓}}$

$\large\green{\texttt{X and Y = Z}}$

$\large\blue{\texttt{Their relation}}$

$\large\blue{\texttt{XY = Z²}}$

$\large\purple{\texttt{Let's carry on}}$

$\large\gray{\texttt{Here we have}}$

$\large\pink{\texttt{X = x + 2}}$

$\large\pink{\texttt{Y = x + 9}}$

$\large\pink{\texttt{Z = x + 5}}$

$\large\purple{\texttt{Now we have to put the values}}$

$\mapsto$ (x+2) (x+9) = (x+5)²

$\mapsto$ x(x+9) +2(x+9) = x² + 10x

+ 25

$\mapsto$ x² + 9x + 2x + 18 = x² +

10x + 25

$\mapsto$ 11x + 18 = 10x + 25

{ We don't write x² here bcz x² = x² cut each other }

$\mapsto$ 11x - 10x = 25 - 18

$\mapsto$ 1x = 7

$\mapsto$ x = 7

$\huge{\boxed{\rm{\red{Explore \: more}}}}$

$\large\mathfrak\orange{Proportion}$

What are proportion ?

Proportion says that two ratios (or fractions) are equal. Example: 1/3 = 2/6.

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Itzbeautyqueen23

Hope it's helpful

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