Let x, y E Rn be given. (a) If ||x|| = ||y|| = 1 and x y = 1, show that x = y. (b) If ||x|| ≤ 1 and ||y|| ≤ 1, prove that √1 - ||x||2²√1 - ||y||² ≤ 1 − |x · y|.

Q: 10. Let h be the function defined by h(x) = x* – 8x3 + 23x2 – 28x + 12. Use the Rational Root…

A: To write the possible rational roots

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A: We know that trigonometry property : Sec2x = 1+tan2x .   We know that general:   1.integration of…

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A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

Q: Let a E K and let f(x) E K[x]. Prove that the remainder when f(x) is divided by x – a is ƒ(a).…

A:

Q: Find all zeroes of f (x) = 4x* – 3x² – x. Check all that apply. - O A) 1 O B) 2 + i C) _ 2 O D) 2 O…

A: Solving the problem by finding the zeros of the function.

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A:

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A: on solving this we get

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A:

Q: P1=(x1,y1,z1) and P2=(x2,y2,z2)  prove that distance of P1 and P2 ; |P1P2|=((x2-x1)2 +(y2-y1)2…

A: Solution: The objective is to prove that the distance of P1 and P2   |P1P2|=((x2-x1)2 +(y2-y1)2…

Q: and

A: Note:  Here, both asked questions are different and not related to each other. As per Guidelines…