If 3x-2-x-7- then 9x2-4-x2- 25493035

The correct option is D 35 3x+2/x=7 Squaring, we get (3x+2/x )^2=(7)^2=49 9x^2+4/x^2+2× 3x×2/x=49 9x^2+4/x^2+12=49 ⇒ 9x^2+4/x^2=49 12=37 (3x 2/x )^2=9x^2+4/x ...

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Byju's Answer

Standard IX

Mathematics

Algebraic Identities

If 3x+2/x=7, ...

Question

$If 3 x + \frac{2}{x} = 7, then (9 x^{2} - \frac{4}{x^{2}})$ =

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Solution

The correct option is B
35

$3 x + \frac{2}{x} = 7 Squaring, we get {(3 x + \frac{2}{x})}^{2} = (7)^{2} = 49 9 x^{2} + \frac{4}{x^{2}} + 2 \times 3 x \times \frac{2}{x} = 49 9 x^{2} + \frac{4}{x^{2}} + 12 = 49 \Rightarrow 9 x^{2} + \frac{4}{x^{2}} = 49 - 12 = 37 {(3 x - \frac{2}{x})}^{2} = 9 x^{2} + \frac{4}{x^{2}} - 2 \times 3 x \times \frac{2}{x} = 9 x^{2} + \frac{4}{x^{2}} - 12 = 37 - 12 = 25 = (5)^{2} ∴ 3 x - \frac{2}{x} = 5 Now, (3 x + \frac{2}{x}) (3 x - \frac{2}{x}) = 7 \times 5 \Rightarrow (3 x)^{2} - {(\frac{2}{x})}^{2} = 35 \Rightarrow 9 x^{2} - \frac{4}{x^{2}} = 35$

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If 3x+2x=7, then (9x2−4x2)=

The correct option is B 35 3x+2x=7Squaring, we get(3x+2x)2=(7)2=499x2+4x2+2×3x×2x=499x2+4x2+12=49⇒ 9x2+4x2=49−12=37(3x−2x)2=9x2+4x2−2×3x×2x=9x2+4x2−12=37−12=25=(5)2∴ 3x−2x=5Now, (3x+2x)(3x−2x)=7×5⇒ (3x)2−(2x)2=35⇒ 9x2−4x2=35

$If 3 x + \frac{2}{x} = 7, then (9 x^{2} - \frac{4}{x^{2}})$ =