If \(\sqrt{5 x+9}+\sqrt{5 x-9}=3(2+\sqrt{2})\), then \(\sqrt{10 x+9}\) is equal to Options: A) \(4 \sqrt{5}\) B) \(2 \sqrt{7}\) C) \(3 \sqrt{31}\) D) \(3 \sqrt{7}\)

D. \(3 \sqrt{7}\). Step 1. Let A=√(5x+9), B=√(5x−9). The sum is 3(2+√2), and A²−B²=18. Step 2. Therefore A−B=18/[3(2+√2)]=3(2−√2).

For some positive and distinct real numbers \(x, y\) and \(z\), if \(\frac{1}{\sqrt{y}+\sqrt{z}}\) is the arithmetic mean of \(\frac{1}{\sqrt{x}+\sqrt{z}}\) and \(\frac{1}{\sqrt{x}+\sqrt{y}}\), then the relationship which will always hold true, is Options: A) \(\sqrt{x}, \sqrt{y}\) and \(\sqrt{z}\) are in arithmetic progression B) \(\sqrt{x}, \sqrt{z}\) and \(\sqrt{y}\) are in arithmetic progression C) \(y, x\) and \(z\) are in arithmetic progression D) \(x, y\) and \(z\) are in arithmetic progression

C. \(y, x\) and \(z\) are in arithmetic progression. Step 1. Let a=√x,b=√y,c=√z. All denominators are positive. Step 2. The mean statement is 2/(b+c)=1/(a+c)+1/(a+b).

CAT Algebra Bible Top 10 Must Solve Algebra Questions covering 100% of Syllabus – Page 3

All 21 Algebra questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 3 of 7.

CAT 2024 Slot 3 · Quant

If \((a+b \sqrt{3})^2=52+30 \sqrt{3}\), where \(a\) and \(b\) are natural numbers, then \(a+b\) equals

CAT 2023 Slot 1 · Quant

If \(\sqrt{5 x+9}+\sqrt{5 x-9}=3(2+\sqrt{2})\), then \(\sqrt{10 x+9}\) is equal to

CAT 2023 Slot 1 · Quant

For some positive and distinct real numbers \(x, y\) and \(z\), if \(\frac{1}{\sqrt{y}+\sqrt{z}}\) is the arithmetic mean of \(\frac{1}{\sqrt{x}+\sqrt{z}}\) and \(\frac{1}{\sqrt{x}+\sqrt{y}}\), then the relationship which will always hold true, is

CAT 2023 Slot 3 · Quant

If \(x\) is a positive real number such that \(x^8+\left(\frac{1}{x}\right)^8=47\), then the value of \(x^9+\left(\frac{1}{x}\right)^9\) is

CAT 2023 Slot 3 · Quant

A quadratic equation \(x^2+b x+c=0\) has two real roots. If the difference between the reciprocals of the roots is \(\frac{1}{3}\), and the sum of the reciprocals of the squares of the roots is \(\frac{5}{9}\), then the largest possible value of \((b+c)\) is

Last day solving checklist

Name the unknown. Include its unit and state whether it is a count, amount, rate or parameter.
Form the relationships. Translate each given condition into an equation or restriction.
Choose the method. Use the formula, substitution, elimination, a sign chart or a bound appropriate to this concept.
Check restrictions. Check integer counts, signs, nonzero denominators, domains and all original conditions.
Verify the answer. Substitute into the original question; for an extreme, show a feasible example reaches it.

All 10 repeating CAT PYQs and how much each adds

CAT PYQ	Repeating CAT PYQ	Questions	Representative	Cumulative questions	Cumulative share
1	Conjugate surds and difference of squares	7	CAT 2021 S1 Q4	7	21.21%
2	Symmetric sums products and reciprocal powers	7	CAT 2022 S3 Q14	14	42.42%
3	Square sum product identities in diagonal geometry	5	CAT 2021 S2 Q9	19	57.58%
4	Complete squares and use sign or equality conditions	4	CAT 2023 S1 Q2	23	69.70%
5	Group common expressions and factor product constraints	4	CAT 2021 S2 Q3	27	81.82%
6	Difference or sum formulas for sequence totals	2	CAT 2021 S2 Q20	29	87.88%
7	Add and subtract values at opposite polynomial roots	1	CAT 2022 S2 Q9	30	90.91%
8	Common base exponent identity for all parameter values	1	CAT 2022 S3 Q11	31	93.94%
9	Square and factor an absolute value inequality	1	CAT 2021 S3 Q18	32	96.97%
10	Expand a nested GP into simpler series	1	CAT 2023 S3 Q20	33	100%

Based on CAT Actual Quant Papers.

CAT Algebra Bible Top 10 Must Solve Algebra Questions covering 100% of Syllabus – Page 3

Solution — first steps

Solution — first steps

Solution — first steps

Solution — first steps

Solution — first steps