Which of the following algebraic expressions are polynomials? If so, find their degree.(a) a + 1/a (e) 5x ^ 2 - 7x ^ 3 + 9 (b) x ^ 2 + 3x + 5 (f) a ^ 3 + a ^ 6 - 5/a + a (c) 9x ^ 2 + 3/x - x ^ 3 (d) p ^ 6 - 1
Answers
Answer:
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Formal Sciences – Like MathematicsANSWER:
Given:
a + b = a × b = a ÷ b
To Find:
Value of a and b
Solution:
We are given that,
\implies\sf a+b=a\times b=a\div b⟹a+b=a×b=a÷b
So,
\implies\sf a\!\!\!/:\times b=\dfrac{a\!\!\!/:\}{b}
\implies\sf b=\dfrac{1}{b}⟹b=
b
1
Transposing b to LHS,
\implies\sf b^2=1⟹b
2
=1
Taking square root,
\implies\sf \sqrt{b^2}=\sqrt1⟹
b
2
=
1
\implies\sf b=\pm1⟹b=±1
So, now we will put the value of b, in any 2 of those equations(one of them will be a + b).
We had,
\implies\sf a+b=a\times b⟹a+b=a×b
Taking b = 1,
\implies\sf a+1=a\times 1⟹a+1=a×1
\implies\sf a+1=a⟹a+1=a
Cancelling a,
\implies\sf a\!\!\!/\:+1=a\!\!\!/\:⟹a/+1=a/
\implies\sf 1=0⟹1=0
As, the staterment is false, b ≠ 1.
Taking b = -1,
\implies\sf a-1=a\times (-1)⟹a−1=a×(−1)
\implies\sf a-1=-a⟹a−1=−a
Transposing -a to LHS,
\implies\sf a+a=1⟹a+a=1
\implies\sf 2a=1⟹2a=1
Transposing 2 to RHS,
\implies\sf a=\dfrac{1}{2}⟹a=
2
1
Hence, for b = -1, a = 1/2.
Therefore value of a = 1/2 and value of b = -1.
Answer:
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