Question

4 ^ x+1 + 4 ^ 1 - x = 10. solve and give me answer 50 point I give. please answer my answwr​

Answer 1

To Solve :-

• $\rm{4^{(x+1)}+4^{(1-x)}=10}$

Solution :-

Given, $\rm{4^{(x+1)}+4^{(1-x)}=10}$

$\implies\rm{4^x.\:4+\dfrac{4}{4^x}=10}$

$\implies\rm{4y+\dfrac{4}{y}=10\quad\quad\quad[Put\:4^x=y]}$

$\implies\rm{4y^2+4=10y}$

$\implies\rm{4y^2-10y+4=0}$

$\implies\rm{2y^2-5y+2=0}$

By splitting the middle term, we get,

$\implies\rm{2y^2-4y-y+2=0}$

$\implies\rm{2y(y-2)-1(y-2)=0}$

$\implies\rm{(y-2)(2y-1)=0}$

$\implies\rm{y-2=0\quad\quad\:or\quad\quad\:2y-1=0}$

$\implies\rm{y=2\quad\quad\quad\quad\:or\quad\quad\:y=\dfrac{1}{2}}$

$\implies\rm{But\:y=4^x}$

$\implies\rm{4^x=2\quad\quad\:or\quad\quad\:4^x=\dfrac{1}{2}}$

$\implies\rm{(2)^{2x}=2^1\:\:or\quad\quad\:(2)^{2x}=(2)^{-1}}$

$\implies\rm{2x=1\quad\quad\:or\quad\quad\:2x=-1}$

$\implies\bold{x=\dfrac{1}{2}\quad\quad\:or\quad\quad\:x=\dfrac{-1}{2}}$

Hence, the value of x : $\rm{\dfrac{1}{2}\:or\:\dfrac{-1}{2}}$

Answer 2

Step-by-step explanation:

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10th

Maths

Pair of Linear Equations in Two Variables

Algebraic Solution of a Pair of Linear Equations

If three times the larger o...

MATHS

If three times the larger of the two numbers is divided by the smaller one, we get 4 as quotient and 3 as the remainder. Also, if seven times the smaller number is divided by the larger one, we get 5 as quotient and 1 as the remainder. Find the numbers.

November 22, 2019avatar

Amber Ghadage

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ANSWER

Let the larger number be x and the smaller one be y. We know that

Dividend =(Divisor × Quotient) +Remainder. (i)

When 3x is divided by y, we get 4 as quotient and 3 as remainder. Therefore, by using (i), we get

3x=4y+3⇒3x−4y−3=0 (ii)

When 7y is divided by x, we get 5 as quotient and 1 as remainder. Therefore, by using (i), we get

7y=5x+1⇒5x−7y+1=0 .(iii)

Solving equations (ii) and (iii), by cross-multiplication, we get

−4−21

x

=

3+15

−y

=

−21+20

1

−25

x

=−1,

18

−y

=−1

⇒x=25 and y=18

Hence, the required numbers are 25 and 18....

hey the answer is for the question 'If three times the larger of the two numbers is divided by the smaller one, we get 4 as quotient and 3 as the remainder. Also, if seven times the smaller number is divided by the larger one, we get 5 as quotient and 1 as the remainder. Find the numbers.' I was not able to answer there, as there was no option to answer. Please don't mind. Here is the answer. Hope you will check it. Please mark me as Brainliest