Question

Two numbers when multiplied equals 45. one number is x and the other number is greater than x by 4 a) Represent the information given in equation form. b) Express as a quadratic equation c) Solve the quadratic equation to find possible values for x d) If told that the two number were positive, give the values of the two original numbers.​

Answer 1

Answer:

Given,

Two numbers when multiplied equals to 45.

One number is x and the other number is greater than x by 4.

So, we can write that,

Solution (a) :

$\pink{ \sf \: one \: number \: = x}$

and

$\sf \: \: \pink{Second \: number \: = x + 4}$

Solution (b+c) :

Now, the product of two numbers is 45.

$\: \: \: \: \: \: \: \: \bf\:x(x + 4) = 45\\</p><p>\sf \implies \:{x}^{2} + 4x = 45\\</p><p>\sf \implies \: {x}^{2} + 4x - 45 = 0\\</p><p>\sf \implies \:{x}^{2} + 9x - 5x - 45 = 0\\</p><p>\sf \implies \:x(x + 9) - 5(x + 9) = 0\\</p><p>\sf \implies \:(x + 9)(x - 5)= 0\\</p><p>\sf \therefore \: \: x = - 9 \: \: \: or \: \: \: x = 5$

But it is given that number is positive.

$\sf \: so \: \: \: x = - 9 \: \: \: is \: \: not \: \: \: \orange{acceptable}$

Therefore,

$\large \: \pink{ \sf \: x = 5}$

Solution (d) :

so,

$\pink{\sf{one \: number = 5}} \\ \pink{\sf{other \: number = 5 + 4 = 9} }$

Answer 2

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There are two numbers :-

• (no. 1)
• (no. 2)

Both get multiplied together and results = 45

$\mathtt \purple{ i.e, }$ $\sf \red{ (no. \: 1 ) \times (no. \: 2 ) = 45 }$

Let the numbers be:-

no. 1 = x and other no. is greater 4 more than no. 1

so it will be x+4.

New Numbers :-

• no. 1 = x
• no. 2 = x+4

(there product) = 45

Putting the values :-

$\rm{ (x) \times (x+4) = 45 }$

$\rm{ x(x+4) = 45 }$

$\rm{ x^{2} + 4x = 45 }$

$\rm{ x^{2} + 4x - 45 = 0 }$

$\rm{ x(x+9) - 5(x+9) = 0 }$

$\rm{ (x+9) (x-5) = 0 }$

$\therefore$ $\sf \red{ x \: = \: -9 \: \: or \: \: x \: = \: 5 }$

But, in the question it is given that the no. is positive, Then we will take $\bf \purple{ x = 5 }$ because it is positive.

The values of two no.s will be :-

5 and 9 because (5+4 = 9) thus, ( 5×9=45)

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