Mathematics: (x+5)1/2=(5-2x)1/4 This equation has two different rational exponents, 1/2 and 1/4 . The inverse powers for these two rational exponents would be 2 and 4, respectively. Will raising both sides to the 2nd power eliminate both rational exponents? Explain.

(x+5)1/2=(5-2x)1/4 This equation has two different

Ответ:

05leslun42715

23.01.2022

Mathematics

Raising both sides to the second power will eliminate only one rational exponent

Step-by-step explanation:

we have

$(x+5)^{\frac{1}{2}}=(5-2x)^{\frac{1}{4}}$

If raising both sides to the 2nd power

$[(x+5)^{\frac{1}{2}}]^2=[(5-2x)^{\frac{1}{4}}]^2$

Remember the property of exponents

$(x^{m} )^{n} =x^{m*n}$

$x^{\frac{m}{n}}=\sqrt[n]{x^m}$

Multiply the exponents

$(x+5)^{\frac{2}{2}}=(5-2x)^{\frac{2}{4}}$

Simplify

$(x+5)=(5-2x)^\frac{1}{2}$

$(x+5)=\sqrt{5-2x}$

therefore

Raising both sides to the second power will eliminate only one rational exponent

To eliminate both rational exponents, both sides must be raised to the fourth power

$[(x+5)^{\frac{1}{2}}]^4=[(5-2x)^{\frac{1}{4}}]^4$

$(x+5)^{\frac{4}{2}}=(5-2x)^{\frac{4}{4}}$

simplify

(x+5)^2=(5-2x)

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Ответ:

kaliyab191

24.01.2023

Mathematics

5,14,23

Step-by-step explanation:

arithmetic sequences are in form:

a(n)=a(o)+d(n-1)

substitute a(3)=23 and a(26)=230

solve and gives

d=0

a(0)=5

a=5+9(n-1)

a(1)=5

a(2)=14

a(3)=23

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(x+5)1/2=(5-2x)1/4 This equation has two different rational exponents, 1/2 and 1/4 . The inverse powers for these two rational exponents would be 2 and 4, respectively. Will raising both sides to the 2nd power eliminate both rational exponents? Explain.

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